### Task: equation
### Problem:
Discover the operator from examples then apply it:
  59,17 -> 42
  54,52 -> 2
  31,21 -> 10
Apply to: 81,45
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  59,17: '+' gives 76; target=42  no
  59,17: '-' gives 42; target=42  MATCH
  59,17: '*' gives 1003; target=42  no
  59,17: 'concat' gives 5917; target=42  no
  59,17: 'rev_concat' gives 1759; target=42  no
  59,17: 'max*min+sum' gives 1079; target=42  no
  59,17: 'digitsum2' gives 484; target=42  no
  54,52: '+' gives 106; target=2  no
  54,52: '-' gives 2; target=2  MATCH
  54,52: '*' gives 2808; target=2  no
  54,52: 'concat' gives 5452; target=2  no
  54,52: 'rev_concat' gives 5254; target=2  no
  54,52: 'max*min+sum' gives 2914; target=2  no
  54,52: 'digitsum2' gives 256; target=2  no
  31,21: '+' gives 52; target=10  no
  31,21: '-' gives 10; target=10  MATCH
  31,21: '*' gives 651; target=10  no
  31,21: 'concat' gives 3121; target=10  no
  31,21: 'rev_concat' gives 2131; target=10  no
  31,21: 'max*min+sum' gives 703; target=10  no
  31,21: 'digitsum2' gives 49; target=10  no
The only operator consistent with all examples is '-'.
Apply to (81, 45):
  result = 36
Final: \boxed{36}


### Task: unit
### Problem:
Convert 82 kilometres to metres.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilometres = 1000 metres.
So 82 kilometres = 82 * 1000 metres.
Compute step by step:
  8 * 10^1 * 1000 = 80000
  running total = 80000
  2 * 10^0 * 1000 = 2000
  running total = 82000
Final: \boxed{82000}


### Task: gravity
### Problem:
A mass of 27 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 27 * 981.
Step-by-step multiplication:
  2 * 10^1 * 981 = 19620
  running total = 19620
  7 * 10^0 * 981 = 6867
  running total = 26487
So F = 26487 centiNewtons = 264.87 N.
Final: \boxed{264.87}


### Task: gravity
### Problem:
A mass of 42 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 42 * 981.
Step-by-step multiplication:
  4 * 10^1 * 981 = 39240
  running total = 39240
  2 * 10^0 * 981 = 1962
  running total = 41202
So F = 41202 centiNewtons = 412.02 N.
Final: \boxed{412.02}


### Task: numeral
### Problem:
Convert the Roman numeral XXIX to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  X = 10  ->  0 + 10 = 10
  X = 10  ->  10 + 10 = 20
  IX = 9  ->  20 + 9 = 29
Final: \boxed{29}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  lfpufibp fsjjpb rsblf uriqp
### Reasoning:
<|cot_start|>Cipher text: lfpufibp fsjjpb rsblf uriqp
Try each candidate Wonderland word against each ciphertext word:
  cipher='lfpufibp' candidate='alice' length-match=False
  cipher='lfpufibp' candidate='rabbit' length-match=False
  cipher='lfpufibp' candidate='hatter' length-match=False
  cipher='lfpufibp' candidate='cheshire' length-match=True  <- assign
  cipher='lfpufibp' candidate='queen' length-match=False
  cipher='lfpufibp' candidate='tea' length-match=False
  cipher='lfpufibp' candidate='cake' length-match=False
  cipher='lfpufibp' candidate='garden' length-match=False
  cipher='lfpufibp' candidate='mushroom' length-match=True
  cipher='lfpufibp' candidate='card' length-match=False
  cipher='lfpufibp' candidate='card' length-match=False
  cipher='lfpufibp' candidate='wonderland' length-match=False
  cipher='lfpufibp' candidate='white' length-match=False
  cipher='lfpufibp' candidate='down' length-match=False
  cipher='lfpufibp' candidate='smile' length-match=False
  cipher='lfpufibp' candidate='smiled' length-match=False
  cipher='lfpufibp' candidate='looking' length-match=False
  cipher='lfpufibp' candidate='glass' length-match=False
  cipher='lfpufibp' candidate='march' length-match=False
  cipher='lfpufibp' candidate='hare' length-match=False
  cipher='lfpufibp' candidate='dormouse' length-match=True
  cipher='fsjjpb' candidate='alice' length-match=False
  cipher='fsjjpb' candidate='rabbit' length-match=True
  cipher='fsjjpb' candidate='hatter' length-match=True  <- assign
  cipher='fsjjpb' candidate='cheshire' length-match=False
  cipher='fsjjpb' candidate='queen' length-match=False
  cipher='fsjjpb' candidate='tea' length-match=False
  cipher='fsjjpb' candidate='cake' length-match=False
  cipher='fsjjpb' candidate='garden' length-match=True
  cipher='fsjjpb' candidate='mushroom' length-match=False
  cipher='fsjjpb' candidate='card' length-match=False
  cipher='fsjjpb' candidate='card' length-match=False
  cipher='fsjjpb' candidate='wonderland' length-match=False
  cipher='fsjjpb' candidate='white' length-match=False
  cipher='fsjjpb' candidate='down' length-match=False
  cipher='fsjjpb' candidate='smile' length-match=False
  cipher='fsjjpb' candidate='smiled' length-match=True
  cipher='fsjjpb' candidate='looking' length-match=False
  cipher='fsjjpb' candidate='glass' length-match=False
  cipher='fsjjpb' candidate='march' length-match=False
  cipher='fsjjpb' candidate='hare' length-match=False
  cipher='fsjjpb' candidate='dormouse' length-match=False
  cipher='rsblf' candidate='alice' length-match=True
  cipher='rsblf' candidate='rabbit' length-match=False
  cipher='rsblf' candidate='hatter' length-match=False
  cipher='rsblf' candidate='cheshire' length-match=False
  cipher='rsblf' candidate='queen' length-match=True
  cipher='rsblf' candidate='tea' length-match=False
  cipher='rsblf' candidate='cake' length-match=False
  cipher='rsblf' candidate='garden' length-match=False
  cipher='rsblf' candidate='mushroom' length-match=False
  cipher='rsblf' candidate='card' length-match=False
  cipher='rsblf' candidate='card' length-match=False
  cipher='rsblf' candidate='wonderland' length-match=False
  cipher='rsblf' candidate='white' length-match=True
  cipher='rsblf' candidate='down' length-match=False
  cipher='rsblf' candidate='smile' length-match=True
  cipher='rsblf' candidate='smiled' length-match=False
  cipher='rsblf' candidate='looking' length-match=False
  cipher='rsblf' candidate='glass' length-match=True
  cipher='rsblf' candidate='march' length-match=True  <- assign
  cipher='rsblf' candidate='hare' length-match=False
  cipher='rsblf' candidate='dormouse' length-match=False
  cipher='uriqp' candidate='alice' length-match=True
  cipher='uriqp' candidate='rabbit' length-match=False
  cipher='uriqp' candidate='hatter' length-match=False
  cipher='uriqp' candidate='cheshire' length-match=False
  cipher='uriqp' candidate='queen' length-match=True
  cipher='uriqp' candidate='tea' length-match=False
  cipher='uriqp' candidate='cake' length-match=False
  cipher='uriqp' candidate='garden' length-match=False
  cipher='uriqp' candidate='mushroom' length-match=False
  cipher='uriqp' candidate='card' length-match=False
  cipher='uriqp' candidate='card' length-match=False
  cipher='uriqp' candidate='wonderland' length-match=False
  cipher='uriqp' candidate='white' length-match=True
  cipher='uriqp' candidate='down' length-match=False
  cipher='uriqp' candidate='smile' length-match=True  <- assign
  cipher='uriqp' candidate='smiled' length-match=False
  cipher='uriqp' candidate='looking' length-match=False
  cipher='uriqp' candidate='glass' length-match=True
  cipher='uriqp' candidate='march' length-match=True
  cipher='uriqp' candidate='hare' length-match=False
  cipher='uriqp' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  cheshire hatter march smile
Final: \boxed{cheshire hatter march smile}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10010001 -> 11001000
  11000000 -> 01100000
  00001011 -> 10000101
Apply to: 11111111
### Reasoning:
<|cot_start|>Given examples:
  10010001 -> 11001000
  11000000 -> 01100000
  00001011 -> 10000101
Compare each bit position across the three examples:
  bit 0: 1,1,0 -> 1,0,1
  bit 1: 0,1,0 -> 1,1,0
  bit 2: 0,0,0 -> 0,1,0
  bit 3: 1,0,0 -> 0,0,0
  bit 4: 0,0,1 -> 1,0,0
  bit 5: 0,0,0 -> 0,0,1
  bit 6: 0,0,1 -> 0,0,0
  bit 7: 1,0,1 -> 0,0,1
Deduce rule: rotate right 1.
Apply to 11111111:
  result = 11111111
Final: \boxed{11111111}


### Task: unit
### Problem:
Convert 94 metres to centimetres.
### Reasoning:
<|cot_start|>Conversion factor: 1 metres = 100 centimetres.
So 94 metres = 94 * 100 centimetres.
Compute step by step:
  9 * 10^1 * 100 = 9000
  running total = 9000
  4 * 10^0 * 100 = 400
  running total = 9400
Final: \boxed{9400}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00010011 -> 11110011
  01010001 -> 11110001
  11110101 -> 11110101
Apply to: 01010000
### Reasoning:
<|cot_start|>Given examples:
  00010011 -> 11110011
  01010001 -> 11110001
  11110101 -> 11110101
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 1,1,1
  bit 1: 0,1,1 -> 1,1,1
  bit 2: 0,0,1 -> 1,1,1
  bit 3: 1,1,1 -> 1,1,1
  bit 4: 0,0,0 -> 0,0,0
  bit 5: 0,0,1 -> 0,0,1
  bit 6: 1,0,0 -> 1,0,0
  bit 7: 1,1,1 -> 1,1,1
Deduce rule: or 0xF0.
Apply to 01010000:
  result = 11110000
Final: \boxed{11110000}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  qtrgbx xdztdcqb hcbbf juzxbf
### Reasoning:
<|cot_start|>Cipher text: qtrgbx xdztdcqb hcbbf juzxbf
Try each candidate Wonderland word against each ciphertext word:
  cipher='qtrgbx' candidate='alice' length-match=False
  cipher='qtrgbx' candidate='rabbit' length-match=True
  cipher='qtrgbx' candidate='hatter' length-match=True
  cipher='qtrgbx' candidate='cheshire' length-match=False
  cipher='qtrgbx' candidate='queen' length-match=False
  cipher='qtrgbx' candidate='tea' length-match=False
  cipher='qtrgbx' candidate='cake' length-match=False
  cipher='qtrgbx' candidate='garden' length-match=True
  cipher='qtrgbx' candidate='mushroom' length-match=False
  cipher='qtrgbx' candidate='card' length-match=False
  cipher='qtrgbx' candidate='card' length-match=False
  cipher='qtrgbx' candidate='wonderland' length-match=False
  cipher='qtrgbx' candidate='white' length-match=False
  cipher='qtrgbx' candidate='down' length-match=False
  cipher='qtrgbx' candidate='smile' length-match=False
  cipher='qtrgbx' candidate='smiled' length-match=True  <- assign
  cipher='qtrgbx' candidate='looking' length-match=False
  cipher='qtrgbx' candidate='glass' length-match=False
  cipher='qtrgbx' candidate='march' length-match=False
  cipher='qtrgbx' candidate='hare' length-match=False
  cipher='qtrgbx' candidate='dormouse' length-match=False
  cipher='xdztdcqb' candidate='alice' length-match=False
  cipher='xdztdcqb' candidate='rabbit' length-match=False
  cipher='xdztdcqb' candidate='hatter' length-match=False
  cipher='xdztdcqb' candidate='cheshire' length-match=True
  cipher='xdztdcqb' candidate='queen' length-match=False
  cipher='xdztdcqb' candidate='tea' length-match=False
  cipher='xdztdcqb' candidate='cake' length-match=False
  cipher='xdztdcqb' candidate='garden' length-match=False
  cipher='xdztdcqb' candidate='mushroom' length-match=True
  cipher='xdztdcqb' candidate='card' length-match=False
  cipher='xdztdcqb' candidate='card' length-match=False
  cipher='xdztdcqb' candidate='wonderland' length-match=False
  cipher='xdztdcqb' candidate='white' length-match=False
  cipher='xdztdcqb' candidate='down' length-match=False
  cipher='xdztdcqb' candidate='smile' length-match=False
  cipher='xdztdcqb' candidate='smiled' length-match=False
  cipher='xdztdcqb' candidate='looking' length-match=False
  cipher='xdztdcqb' candidate='glass' length-match=False
  cipher='xdztdcqb' candidate='march' length-match=False
  cipher='xdztdcqb' candidate='hare' length-match=False
  cipher='xdztdcqb' candidate='dormouse' length-match=True  <- assign
  cipher='hcbbf' candidate='alice' length-match=True
  cipher='hcbbf' candidate='rabbit' length-match=False
  cipher='hcbbf' candidate='hatter' length-match=False
  cipher='hcbbf' candidate='cheshire' length-match=False
  cipher='hcbbf' candidate='queen' length-match=True  <- assign
  cipher='hcbbf' candidate='tea' length-match=False
  cipher='hcbbf' candidate='cake' length-match=False
  cipher='hcbbf' candidate='garden' length-match=False
  cipher='hcbbf' candidate='mushroom' length-match=False
  cipher='hcbbf' candidate='card' length-match=False
  cipher='hcbbf' candidate='card' length-match=False
  cipher='hcbbf' candidate='wonderland' length-match=False
  cipher='hcbbf' candidate='white' length-match=True
  cipher='hcbbf' candidate='down' length-match=False
  cipher='hcbbf' candidate='smile' length-match=True
  cipher='hcbbf' candidate='smiled' length-match=False
  cipher='hcbbf' candidate='looking' length-match=False
  cipher='hcbbf' candidate='glass' length-match=True
  cipher='hcbbf' candidate='march' length-match=True
  cipher='hcbbf' candidate='hare' length-match=False
  cipher='hcbbf' candidate='dormouse' length-match=False
  cipher='juzxbf' candidate='alice' length-match=False
  cipher='juzxbf' candidate='rabbit' length-match=True
  cipher='juzxbf' candidate='hatter' length-match=True
  cipher='juzxbf' candidate='cheshire' length-match=False
  cipher='juzxbf' candidate='queen' length-match=False
  cipher='juzxbf' candidate='tea' length-match=False
  cipher='juzxbf' candidate='cake' length-match=False
  cipher='juzxbf' candidate='garden' length-match=True  <- assign
  cipher='juzxbf' candidate='mushroom' length-match=False
  cipher='juzxbf' candidate='card' length-match=False
  cipher='juzxbf' candidate='card' length-match=False
  cipher='juzxbf' candidate='wonderland' length-match=False
  cipher='juzxbf' candidate='white' length-match=False
  cipher='juzxbf' candidate='down' length-match=False
  cipher='juzxbf' candidate='smile' length-match=False
  cipher='juzxbf' candidate='smiled' length-match=True
  cipher='juzxbf' candidate='looking' length-match=False
  cipher='juzxbf' candidate='glass' length-match=False
  cipher='juzxbf' candidate='march' length-match=False
  cipher='juzxbf' candidate='hare' length-match=False
  cipher='juzxbf' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  smiled dormouse queen garden
Final: \boxed{smiled dormouse queen garden}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00111011 -> 01110110
  01111100 -> 11111000
  10110100 -> 01101001
Apply to: 11001100
### Reasoning:
<|cot_start|>Given examples:
  00111011 -> 01110110
  01111100 -> 11111000
  10110100 -> 01101001
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 0,1,0
  bit 1: 0,1,0 -> 1,1,1
  bit 2: 1,1,1 -> 1,1,1
  bit 3: 1,1,1 -> 1,1,0
  bit 4: 1,1,0 -> 0,1,1
  bit 5: 0,1,1 -> 1,0,0
  bit 6: 1,0,0 -> 1,0,0
  bit 7: 1,0,0 -> 0,0,1
Deduce rule: rotate left 1.
Apply to 11001100:
  result = 10011001
Final: \boxed{10011001}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00111110 -> 11000001
  00110011 -> 11001100
  10011110 -> 01100001
Apply to: 00101010
### Reasoning:
<|cot_start|>Given examples:
  00111110 -> 11000001
  00110011 -> 11001100
  10011110 -> 01100001
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 1,1,0
  bit 1: 0,0,0 -> 1,1,1
  bit 2: 1,1,0 -> 0,0,1
  bit 3: 1,1,1 -> 0,0,0
  bit 4: 1,0,1 -> 0,1,0
  bit 5: 1,0,1 -> 0,1,0
  bit 6: 1,1,1 -> 0,0,0
  bit 7: 0,1,0 -> 1,0,1
Deduce rule: invert (NOT).
Apply to 00101010:
  result = 11010101
Final: \boxed{11010101}


### Task: gravity
### Problem:
A mass of 50 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 50 * 981.
Step-by-step multiplication:
  5 * 10^1 * 981 = 49050
  running total = 49050
  0 * 10^0 * 981 = 0
  running total = 49050
So F = 49050 centiNewtons = 490.50 N.
Final: \boxed{490.50}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  45,63 -> 4563
  37,75 -> 3775
  23,88 -> 2388
Apply to: 56,91
### Reasoning:
<|cot_start|>Examples:
  45,63 -> 4563
  37,75 -> 3775
  23,88 -> 2388
Check both candidate forms:
  concat(45,63)=4563  rev_concat(45,63)=6345  target=4563  concat
  concat(37,75)=3775  rev_concat(37,75)=7537  target=3775  concat
  concat(23,88)=2388  rev_concat(23,88)=8823  target=2388  concat
Conclude operator: concat.
Apply to (56, 91):  answer = 5691
Final: \boxed{5691}


### Task: numeral
### Problem:
Convert the Roman numeral XI to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  X = 10  ->  0 + 10 = 10
  I = 1  ->  10 + 1 = 11
Final: \boxed{11}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11010111 -> 11101011
  10100100 -> 01010010
  11011001 -> 11101100
Apply to: 11111011
### Reasoning:
<|cot_start|>Given examples:
  11010111 -> 11101011
  10100100 -> 01010010
  11011001 -> 11101100
Compare each bit position across the three examples:
  bit 0: 1,1,1 -> 1,0,1
  bit 1: 1,0,1 -> 1,1,1
  bit 2: 0,1,0 -> 1,0,1
  bit 3: 1,0,1 -> 0,1,0
  bit 4: 0,0,1 -> 1,0,1
  bit 5: 1,1,0 -> 0,0,1
  bit 6: 1,0,0 -> 1,1,0
  bit 7: 1,0,1 -> 1,0,0
Deduce rule: rotate right 1.
Apply to 11111011:
  result = 11111101
Final: \boxed{11111101}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  71,55 -> 7155
  42,65 -> 4265
  32,14 -> 3214
Apply to: 77,32
### Reasoning:
<|cot_start|>Examples:
  71,55 -> 7155
  42,65 -> 4265
  32,14 -> 3214
Check both candidate forms:
  concat(71,55)=7155  rev_concat(71,55)=5571  target=7155  concat
  concat(42,65)=4265  rev_concat(42,65)=6542  target=4265  concat
  concat(32,14)=3214  rev_concat(32,14)=1432  target=3214  concat
Conclude operator: concat.
Apply to (77, 32):  answer = 7732
Final: \boxed{7732}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  44,63 -> 6344
  17,41 -> 4117
  85,44 -> 4485
Apply to: 34,53
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  44,63: '+' gives 107; target=6344  no
  44,63: '-' gives 19; target=6344  no
  44,63: '*' gives 2772; target=6344  no
  44,63: 'concat' gives 4463; target=6344  no
  44,63: 'rev_concat' gives 6344; target=6344  MATCH
  44,63: 'max*min+sum' gives 2879; target=6344  no
  44,63: 'digitsum2' gives 289; target=6344  no
  17,41: '+' gives 58; target=4117  no
  17,41: '-' gives 24; target=4117  no
  17,41: '*' gives 697; target=4117  no
  17,41: 'concat' gives 1741; target=4117  no
  17,41: 'rev_concat' gives 4117; target=4117  MATCH
  17,41: 'max*min+sum' gives 755; target=4117  no
  17,41: 'digitsum2' gives 169; target=4117  no
  85,44: '+' gives 129; target=4485  no
  85,44: '-' gives 41; target=4485  no
  85,44: '*' gives 3740; target=4485  no
  85,44: 'concat' gives 8544; target=4485  no
  85,44: 'rev_concat' gives 4485; target=4485  MATCH
  85,44: 'max*min+sum' gives 3869; target=4485  no
  85,44: 'digitsum2' gives 441; target=4485  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (34, 53):
  result = 5334
Final: \boxed{5334}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00101000 -> 00010100
  10101011 -> 11010101
  11010101 -> 11101010
Apply to: 00000011
### Reasoning:
<|cot_start|>Given examples:
  00101000 -> 00010100
  10101011 -> 11010101
  11010101 -> 11101010
Compare each bit position across the three examples:
  bit 0: 0,1,1 -> 0,1,1
  bit 1: 0,0,1 -> 0,1,1
  bit 2: 1,1,0 -> 0,0,1
  bit 3: 0,0,1 -> 1,1,0
  bit 4: 1,1,0 -> 0,0,1
  bit 5: 0,0,1 -> 1,1,0
  bit 6: 0,1,0 -> 0,0,1
  bit 7: 0,1,1 -> 0,1,0
Deduce rule: rotate right 1.
Apply to 00000011:
  result = 10000001
Final: \boxed{10000001}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  93,78 -> 7425
  50,93 -> 4793
  99,73 -> 7399
Apply to: 88,74
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  93,78: '+' gives 171; target=7425  no
  93,78: '-' gives 15; target=7425  no
  93,78: '*' gives 7254; target=7425  no
  93,78: 'concat' gives 9378; target=7425  no
  93,78: 'rev_concat' gives 7893; target=7425  no
  93,78: 'max*min+sum' gives 7425; target=7425  MATCH
  93,78: 'digitsum2' gives 729; target=7425  no
  50,93: '+' gives 143; target=4793  no
  50,93: '-' gives 43; target=4793  no
  50,93: '*' gives 4650; target=4793  no
  50,93: 'concat' gives 5093; target=4793  no
  50,93: 'rev_concat' gives 9350; target=4793  no
  50,93: 'max*min+sum' gives 4793; target=4793  MATCH
  50,93: 'digitsum2' gives 289; target=4793  no
  99,73: '+' gives 172; target=7399  no
  99,73: '-' gives 26; target=7399  no
  99,73: '*' gives 7227; target=7399  no
  99,73: 'concat' gives 9973; target=7399  no
  99,73: 'rev_concat' gives 7399; target=7399  MATCH
  99,73: 'max*min+sum' gives 7399; target=7399  MATCH
  99,73: 'digitsum2' gives 784; target=7399  no
The only operator consistent with all examples is 'max*min+sum'.
Apply to (88, 74):
  result = 6674
Final: \boxed{6674}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01110111 -> 11101110
  01100101 -> 10100110
  00010000 -> 00001000
Apply to: 01100001
### Reasoning:
<|cot_start|>Given examples:
  01110111 -> 11101110
  01100101 -> 10100110
  00010000 -> 00001000
Compare each bit position across the three examples:
  bit 0: 0,0,0 -> 1,1,0
  bit 1: 1,1,0 -> 1,0,0
  bit 2: 1,1,0 -> 1,1,0
  bit 3: 1,0,1 -> 0,0,0
  bit 4: 0,0,0 -> 1,0,1
  bit 5: 1,1,0 -> 1,1,0
  bit 6: 1,0,0 -> 1,1,0
  bit 7: 1,1,0 -> 0,0,0
Deduce rule: reverse bits.
Apply to 01100001:
  result = 10000110
Final: \boxed{10000110}


### Task: numeral
### Problem:
Convert the Roman numeral XII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  X = 10  ->  0 + 10 = 10
  I = 1  ->  10 + 1 = 11
  I = 1  ->  11 + 1 = 12
Final: \boxed{12}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  48,55 -> 103
  26,69 -> 95
  57,15 -> 72
Apply to: 52,23
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  48,55: '+' gives 103; target=103  MATCH
  48,55: '-' gives 7; target=103  no
  48,55: '*' gives 2640; target=103  no
  48,55: 'concat' gives 4855; target=103  no
  48,55: 'rev_concat' gives 5548; target=103  no
  48,55: 'max*min+sum' gives 2743; target=103  no
  48,55: 'digitsum2' gives 484; target=103  no
  26,69: '+' gives 95; target=95  MATCH
  26,69: '-' gives 43; target=95  no
  26,69: '*' gives 1794; target=95  no
  26,69: 'concat' gives 2669; target=95  no
  26,69: 'rev_concat' gives 6926; target=95  no
  26,69: 'max*min+sum' gives 1889; target=95  no
  26,69: 'digitsum2' gives 529; target=95  no
  57,15: '+' gives 72; target=72  MATCH
  57,15: '-' gives 42; target=72  no
  57,15: '*' gives 855; target=72  no
  57,15: 'concat' gives 5715; target=72  no
  57,15: 'rev_concat' gives 1557; target=72  no
  57,15: 'max*min+sum' gives 927; target=72  no
  57,15: 'digitsum2' gives 324; target=72  no
The only operator consistent with all examples is '+'.
Apply to (52, 23):
  result = 75
Final: \boxed{75}


### Task: numeral
### Problem:
Convert the Roman numeral XCVIII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  XC = 90  ->  0 + 90 = 90
  V = 5  ->  90 + 5 = 95
  I = 1  ->  95 + 1 = 96
  I = 1  ->  96 + 1 = 97
  I = 1  ->  97 + 1 = 98
Final: \boxed{98}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  74,11 -> 1174
  76,18 -> 1876
  94,63 -> 6394
Apply to: 94,24
### Reasoning:
<|cot_start|>Examples:
  74,11 -> 1174
  76,18 -> 1876
  94,63 -> 6394
Check both candidate forms:
  concat(74,11)=7411  rev_concat(74,11)=1174  target=1174  rev_concat
  concat(76,18)=7618  rev_concat(76,18)=1876  target=1876  rev_concat
  concat(94,63)=9463  rev_concat(94,63)=6394  target=6394  rev_concat
Conclude operator: rev_concat.
Apply to (94, 24):  answer = 2494
Final: \boxed{2494}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  95,94 -> 9594
  15,38 -> 1538
  66,90 -> 6690
Apply to: 74,62
### Reasoning:
<|cot_start|>Examples:
  95,94 -> 9594
  15,38 -> 1538
  66,90 -> 6690
Check both candidate forms:
  concat(95,94)=9594  rev_concat(95,94)=9495  target=9594  concat
  concat(15,38)=1538  rev_concat(15,38)=3815  target=1538  concat
  concat(66,90)=6690  rev_concat(66,90)=9066  target=6690  concat
Conclude operator: concat.
Apply to (74, 62):  answer = 7462
Final: \boxed{7462}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  17,73 -> 7317
  19,12 -> 1219
  93,16 -> 1693
Apply to: 86,34
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  17,73: '+' gives 90; target=7317  no
  17,73: '-' gives 56; target=7317  no
  17,73: '*' gives 1241; target=7317  no
  17,73: 'concat' gives 1773; target=7317  no
  17,73: 'rev_concat' gives 7317; target=7317  MATCH
  17,73: 'max*min+sum' gives 1331; target=7317  no
  17,73: 'digitsum2' gives 324; target=7317  no
  19,12: '+' gives 31; target=1219  no
  19,12: '-' gives 7; target=1219  no
  19,12: '*' gives 228; target=1219  no
  19,12: 'concat' gives 1912; target=1219  no
  19,12: 'rev_concat' gives 1219; target=1219  MATCH
  19,12: 'max*min+sum' gives 259; target=1219  no
  19,12: 'digitsum2' gives 169; target=1219  no
  93,16: '+' gives 109; target=1693  no
  93,16: '-' gives 77; target=1693  no
  93,16: '*' gives 1488; target=1693  no
  93,16: 'concat' gives 9316; target=1693  no
  93,16: 'rev_concat' gives 1693; target=1693  MATCH
  93,16: 'max*min+sum' gives 1597; target=1693  no
  93,16: 'digitsum2' gives 361; target=1693  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (86, 34):
  result = 3486
Final: \boxed{3486}


### Task: gravity
### Problem:
A mass of 3 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 3 * 981.
Step-by-step multiplication:
  3 * 10^0 * 981 = 2943
  running total = 2943
So F = 2943 centiNewtons = 29.43 N.
Final: \boxed{29.43}


### Task: gravity
### Problem:
A mass of 44 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 44 * 981.
Step-by-step multiplication:
  4 * 10^1 * 981 = 39240
  running total = 39240
  4 * 10^0 * 981 = 3924
  running total = 43164
So F = 43164 centiNewtons = 431.64 N.
Final: \boxed{431.64}


### Task: unit
### Problem:
Convert 51 litres to millilitres.
### Reasoning:
<|cot_start|>Conversion factor: 1 litres = 1000 millilitres.
So 51 litres = 51 * 1000 millilitres.
Compute step by step:
  5 * 10^1 * 1000 = 50000
  running total = 50000
  1 * 10^0 * 1000 = 1000
  running total = 51000
Final: \boxed{51000}


### Task: numeral
### Problem:
Convert the Roman numeral LXXXVI to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  X = 10  ->  50 + 10 = 60
  X = 10  ->  60 + 10 = 70
  X = 10  ->  70 + 10 = 80
  V = 5  ->  80 + 5 = 85
  I = 1  ->  85 + 1 = 86
Final: \boxed{86}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  96,45 -> 4596
  21,86 -> 8621
  84,33 -> 3384
Apply to: 23,68
### Reasoning:
<|cot_start|>Examples:
  96,45 -> 4596
  21,86 -> 8621
  84,33 -> 3384
Check both candidate forms:
  concat(96,45)=9645  rev_concat(96,45)=4596  target=4596  rev_concat
  concat(21,86)=2186  rev_concat(21,86)=8621  target=8621  rev_concat
  concat(84,33)=8433  rev_concat(84,33)=3384  target=3384  rev_concat
Conclude operator: rev_concat.
Apply to (23, 68):  answer = 6823
Final: \boxed{6823}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  15,56 -> 289
  75,43 -> 361
  60,78 -> 441
Apply to: 93,86
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  15,56: '+' gives 71; target=289  no
  15,56: '-' gives 41; target=289  no
  15,56: '*' gives 840; target=289  no
  15,56: 'concat' gives 1556; target=289  no
  15,56: 'rev_concat' gives 5615; target=289  no
  15,56: 'max*min+sum' gives 911; target=289  no
  15,56: 'digitsum2' gives 289; target=289  MATCH
  75,43: '+' gives 118; target=361  no
  75,43: '-' gives 32; target=361  no
  75,43: '*' gives 3225; target=361  no
  75,43: 'concat' gives 7543; target=361  no
  75,43: 'rev_concat' gives 4375; target=361  no
  75,43: 'max*min+sum' gives 3343; target=361  no
  75,43: 'digitsum2' gives 361; target=361  MATCH
  60,78: '+' gives 138; target=441  no
  60,78: '-' gives 18; target=441  no
  60,78: '*' gives 4680; target=441  no
  60,78: 'concat' gives 6078; target=441  no
  60,78: 'rev_concat' gives 7860; target=441  no
  60,78: 'max*min+sum' gives 4818; target=441  no
  60,78: 'digitsum2' gives 441; target=441  MATCH
The only operator consistent with all examples is 'digitsum2'.
Apply to (93, 86):
  result = 676
Final: \boxed{676}


### Task: unit
### Problem:
Convert 1 kilometres to metres.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilometres = 1000 metres.
So 1 kilometres = 1 * 1000 metres.
Compute step by step:
  1 * 10^0 * 1000 = 1000
  running total = 1000
Final: \boxed{1000}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11000001 -> 10010100
  10111110 -> 11101011
  10100101 -> 11110000
Apply to: 11001000
### Reasoning:
<|cot_start|>Given examples:
  11000001 -> 10010100
  10111110 -> 11101011
  10100101 -> 11110000
Compare each bit position across the three examples:
  bit 0: 1,1,1 -> 1,1,1
  bit 1: 1,0,0 -> 0,1,1
  bit 2: 0,1,1 -> 0,1,1
  bit 3: 0,1,0 -> 1,0,1
  bit 4: 0,1,0 -> 0,1,0
  bit 5: 0,1,1 -> 1,0,0
  bit 6: 0,1,0 -> 0,1,0
  bit 7: 1,0,1 -> 0,1,0
Deduce rule: xor 0x55.
Apply to 11001000:
  result = 10011101
Final: \boxed{10011101}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  qltflrwe khnnet qlbd achww
### Reasoning:
<|cot_start|>Cipher text: qltflrwe khnnet qlbd achww
Try each candidate Wonderland word against each ciphertext word:
  cipher='qltflrwe' candidate='alice' length-match=False
  cipher='qltflrwe' candidate='rabbit' length-match=False
  cipher='qltflrwe' candidate='hatter' length-match=False
  cipher='qltflrwe' candidate='cheshire' length-match=True
  cipher='qltflrwe' candidate='queen' length-match=False
  cipher='qltflrwe' candidate='tea' length-match=False
  cipher='qltflrwe' candidate='cake' length-match=False
  cipher='qltflrwe' candidate='garden' length-match=False
  cipher='qltflrwe' candidate='mushroom' length-match=True
  cipher='qltflrwe' candidate='card' length-match=False
  cipher='qltflrwe' candidate='card' length-match=False
  cipher='qltflrwe' candidate='wonderland' length-match=False
  cipher='qltflrwe' candidate='white' length-match=False
  cipher='qltflrwe' candidate='down' length-match=False
  cipher='qltflrwe' candidate='smile' length-match=False
  cipher='qltflrwe' candidate='smiled' length-match=False
  cipher='qltflrwe' candidate='looking' length-match=False
  cipher='qltflrwe' candidate='glass' length-match=False
  cipher='qltflrwe' candidate='march' length-match=False
  cipher='qltflrwe' candidate='hare' length-match=False
  cipher='qltflrwe' candidate='dormouse' length-match=True  <- assign
  cipher='khnnet' candidate='alice' length-match=False
  cipher='khnnet' candidate='rabbit' length-match=True
  cipher='khnnet' candidate='hatter' length-match=True  <- assign
  cipher='khnnet' candidate='cheshire' length-match=False
  cipher='khnnet' candidate='queen' length-match=False
  cipher='khnnet' candidate='tea' length-match=False
  cipher='khnnet' candidate='cake' length-match=False
  cipher='khnnet' candidate='garden' length-match=True
  cipher='khnnet' candidate='mushroom' length-match=False
  cipher='khnnet' candidate='card' length-match=False
  cipher='khnnet' candidate='card' length-match=False
  cipher='khnnet' candidate='wonderland' length-match=False
  cipher='khnnet' candidate='white' length-match=False
  cipher='khnnet' candidate='down' length-match=False
  cipher='khnnet' candidate='smile' length-match=False
  cipher='khnnet' candidate='smiled' length-match=True
  cipher='khnnet' candidate='looking' length-match=False
  cipher='khnnet' candidate='glass' length-match=False
  cipher='khnnet' candidate='march' length-match=False
  cipher='khnnet' candidate='hare' length-match=False
  cipher='khnnet' candidate='dormouse' length-match=False
  cipher='qlbd' candidate='alice' length-match=False
  cipher='qlbd' candidate='rabbit' length-match=False
  cipher='qlbd' candidate='hatter' length-match=False
  cipher='qlbd' candidate='cheshire' length-match=False
  cipher='qlbd' candidate='queen' length-match=False
  cipher='qlbd' candidate='tea' length-match=False
  cipher='qlbd' candidate='cake' length-match=True
  cipher='qlbd' candidate='garden' length-match=False
  cipher='qlbd' candidate='mushroom' length-match=False
  cipher='qlbd' candidate='card' length-match=True
  cipher='qlbd' candidate='card' length-match=True
  cipher='qlbd' candidate='wonderland' length-match=False
  cipher='qlbd' candidate='white' length-match=False
  cipher='qlbd' candidate='down' length-match=True  <- assign
  cipher='qlbd' candidate='smile' length-match=False
  cipher='qlbd' candidate='smiled' length-match=False
  cipher='qlbd' candidate='looking' length-match=False
  cipher='qlbd' candidate='glass' length-match=False
  cipher='qlbd' candidate='march' length-match=False
  cipher='qlbd' candidate='hare' length-match=True
  cipher='qlbd' candidate='dormouse' length-match=False
  cipher='achww' candidate='alice' length-match=True
  cipher='achww' candidate='rabbit' length-match=False
  cipher='achww' candidate='hatter' length-match=False
  cipher='achww' candidate='cheshire' length-match=False
  cipher='achww' candidate='queen' length-match=True
  cipher='achww' candidate='tea' length-match=False
  cipher='achww' candidate='cake' length-match=False
  cipher='achww' candidate='garden' length-match=False
  cipher='achww' candidate='mushroom' length-match=False
  cipher='achww' candidate='card' length-match=False
  cipher='achww' candidate='card' length-match=False
  cipher='achww' candidate='wonderland' length-match=False
  cipher='achww' candidate='white' length-match=True
  cipher='achww' candidate='down' length-match=False
  cipher='achww' candidate='smile' length-match=True
  cipher='achww' candidate='smiled' length-match=False
  cipher='achww' candidate='looking' length-match=False
  cipher='achww' candidate='glass' length-match=True  <- assign
  cipher='achww' candidate='march' length-match=True
  cipher='achww' candidate='hare' length-match=False
  cipher='achww' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  dormouse hatter down glass
Final: \boxed{dormouse hatter down glass}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  50,95 -> 9550
  85,39 -> 3985
  25,64 -> 6425
Apply to: 63,95
### Reasoning:
<|cot_start|>Examples:
  50,95 -> 9550
  85,39 -> 3985
  25,64 -> 6425
Check both candidate forms:
  concat(50,95)=5095  rev_concat(50,95)=9550  target=9550  rev_concat
  concat(85,39)=8539  rev_concat(85,39)=3985  target=3985  rev_concat
  concat(25,64)=2564  rev_concat(25,64)=6425  target=6425  rev_concat
Conclude operator: rev_concat.
Apply to (63, 95):  answer = 9563
Final: \boxed{9563}


### Task: numeral
### Problem:
Convert the Roman numeral XLIII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  XL = 40  ->  0 + 40 = 40
  I = 1  ->  40 + 1 = 41
  I = 1  ->  41 + 1 = 42
  I = 1  ->  42 + 1 = 43
Final: \boxed{43}


### Task: unit
### Problem:
Convert 11 litres to millilitres.
### Reasoning:
<|cot_start|>Conversion factor: 1 litres = 1000 millilitres.
So 11 litres = 11 * 1000 millilitres.
Compute step by step:
  1 * 10^1 * 1000 = 10000
  running total = 10000
  1 * 10^0 * 1000 = 1000
  running total = 11000
Final: \boxed{11000}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  rykkea gyzu vmrsmjhu gyrv
### Reasoning:
<|cot_start|>Cipher text: rykkea gyzu vmrsmjhu gyrv
Try each candidate Wonderland word against each ciphertext word:
  cipher='rykkea' candidate='alice' length-match=False
  cipher='rykkea' candidate='rabbit' length-match=True  <- assign
  cipher='rykkea' candidate='hatter' length-match=True
  cipher='rykkea' candidate='cheshire' length-match=False
  cipher='rykkea' candidate='queen' length-match=False
  cipher='rykkea' candidate='tea' length-match=False
  cipher='rykkea' candidate='cake' length-match=False
  cipher='rykkea' candidate='garden' length-match=True
  cipher='rykkea' candidate='mushroom' length-match=False
  cipher='rykkea' candidate='card' length-match=False
  cipher='rykkea' candidate='card' length-match=False
  cipher='rykkea' candidate='wonderland' length-match=False
  cipher='rykkea' candidate='white' length-match=False
  cipher='rykkea' candidate='down' length-match=False
  cipher='rykkea' candidate='smile' length-match=False
  cipher='rykkea' candidate='smiled' length-match=True
  cipher='rykkea' candidate='looking' length-match=False
  cipher='rykkea' candidate='glass' length-match=False
  cipher='rykkea' candidate='march' length-match=False
  cipher='rykkea' candidate='hare' length-match=False
  cipher='rykkea' candidate='dormouse' length-match=False
  cipher='gyzu' candidate='alice' length-match=False
  cipher='gyzu' candidate='rabbit' length-match=False
  cipher='gyzu' candidate='hatter' length-match=False
  cipher='gyzu' candidate='cheshire' length-match=False
  cipher='gyzu' candidate='queen' length-match=False
  cipher='gyzu' candidate='tea' length-match=False
  cipher='gyzu' candidate='cake' length-match=True  <- assign
  cipher='gyzu' candidate='garden' length-match=False
  cipher='gyzu' candidate='mushroom' length-match=False
  cipher='gyzu' candidate='card' length-match=True
  cipher='gyzu' candidate='card' length-match=True
  cipher='gyzu' candidate='wonderland' length-match=False
  cipher='gyzu' candidate='white' length-match=False
  cipher='gyzu' candidate='down' length-match=True
  cipher='gyzu' candidate='smile' length-match=False
  cipher='gyzu' candidate='smiled' length-match=False
  cipher='gyzu' candidate='looking' length-match=False
  cipher='gyzu' candidate='glass' length-match=False
  cipher='gyzu' candidate='march' length-match=False
  cipher='gyzu' candidate='hare' length-match=True
  cipher='gyzu' candidate='dormouse' length-match=False
  cipher='vmrsmjhu' candidate='alice' length-match=False
  cipher='vmrsmjhu' candidate='rabbit' length-match=False
  cipher='vmrsmjhu' candidate='hatter' length-match=False
  cipher='vmrsmjhu' candidate='cheshire' length-match=True
  cipher='vmrsmjhu' candidate='queen' length-match=False
  cipher='vmrsmjhu' candidate='tea' length-match=False
  cipher='vmrsmjhu' candidate='cake' length-match=False
  cipher='vmrsmjhu' candidate='garden' length-match=False
  cipher='vmrsmjhu' candidate='mushroom' length-match=True
  cipher='vmrsmjhu' candidate='card' length-match=False
  cipher='vmrsmjhu' candidate='card' length-match=False
  cipher='vmrsmjhu' candidate='wonderland' length-match=False
  cipher='vmrsmjhu' candidate='white' length-match=False
  cipher='vmrsmjhu' candidate='down' length-match=False
  cipher='vmrsmjhu' candidate='smile' length-match=False
  cipher='vmrsmjhu' candidate='smiled' length-match=False
  cipher='vmrsmjhu' candidate='looking' length-match=False
  cipher='vmrsmjhu' candidate='glass' length-match=False
  cipher='vmrsmjhu' candidate='march' length-match=False
  cipher='vmrsmjhu' candidate='hare' length-match=False
  cipher='vmrsmjhu' candidate='dormouse' length-match=True  <- assign
  cipher='gyrv' candidate='alice' length-match=False
  cipher='gyrv' candidate='rabbit' length-match=False
  cipher='gyrv' candidate='hatter' length-match=False
  cipher='gyrv' candidate='cheshire' length-match=False
  cipher='gyrv' candidate='queen' length-match=False
  cipher='gyrv' candidate='tea' length-match=False
  cipher='gyrv' candidate='cake' length-match=True
  cipher='gyrv' candidate='garden' length-match=False
  cipher='gyrv' candidate='mushroom' length-match=False
  cipher='gyrv' candidate='card' length-match=True  <- assign
  cipher='gyrv' candidate='card' length-match=True  <- assign
  cipher='gyrv' candidate='wonderland' length-match=False
  cipher='gyrv' candidate='white' length-match=False
  cipher='gyrv' candidate='down' length-match=True
  cipher='gyrv' candidate='smile' length-match=False
  cipher='gyrv' candidate='smiled' length-match=False
  cipher='gyrv' candidate='looking' length-match=False
  cipher='gyrv' candidate='glass' length-match=False
  cipher='gyrv' candidate='march' length-match=False
  cipher='gyrv' candidate='hare' length-match=True
  cipher='gyrv' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  rabbit cake dormouse card
Final: \boxed{rabbit cake dormouse card}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01010111 -> 10101011
  11100110 -> 01110011
  11001100 -> 01100110
Apply to: 00000111
### Reasoning:
<|cot_start|>Given examples:
  01010111 -> 10101011
  11100110 -> 01110011
  11001100 -> 01100110
Compare each bit position across the three examples:
  bit 0: 0,1,1 -> 1,0,0
  bit 1: 1,1,1 -> 0,1,1
  bit 2: 0,1,0 -> 1,1,1
  bit 3: 1,0,0 -> 0,1,0
  bit 4: 0,0,1 -> 1,0,0
  bit 5: 1,1,1 -> 0,0,1
  bit 6: 1,1,0 -> 1,1,1
  bit 7: 1,0,0 -> 1,1,0
Deduce rule: rotate right 1.
Apply to 00000111:
  result = 10000011
Final: \boxed{10000011}


### Task: numeral
### Problem:
Convert the Roman numeral XIV to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  X = 10  ->  0 + 10 = 10
  IV = 4  ->  10 + 4 = 14
Final: \boxed{14}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01000010 -> 01000010
  00101001 -> 10010100
  00010001 -> 10001000
Apply to: 01111111
### Reasoning:
<|cot_start|>Given examples:
  01000010 -> 01000010
  00101001 -> 10010100
  00010001 -> 10001000
Compare each bit position across the three examples:
  bit 0: 0,0,0 -> 0,1,1
  bit 1: 1,0,0 -> 1,0,0
  bit 2: 0,1,0 -> 0,0,0
  bit 3: 0,0,1 -> 0,1,0
  bit 4: 0,1,0 -> 0,0,1
  bit 5: 0,0,0 -> 0,1,0
  bit 6: 1,0,0 -> 1,0,0
  bit 7: 0,1,1 -> 0,0,0
Deduce rule: reverse bits.
Apply to 01111111:
  result = 11111110
Final: \boxed{11111110}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  52,64 -> 12
  85,25 -> 60
  52,18 -> 34
Apply to: 71,87
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  52,64: '+' gives 116; target=12  no
  52,64: '-' gives 12; target=12  MATCH
  52,64: '*' gives 3328; target=12  no
  52,64: 'concat' gives 5264; target=12  no
  52,64: 'rev_concat' gives 6452; target=12  no
  52,64: 'max*min+sum' gives 3444; target=12  no
  52,64: 'digitsum2' gives 289; target=12  no
  85,25: '+' gives 110; target=60  no
  85,25: '-' gives 60; target=60  MATCH
  85,25: '*' gives 2125; target=60  no
  85,25: 'concat' gives 8525; target=60  no
  85,25: 'rev_concat' gives 2585; target=60  no
  85,25: 'max*min+sum' gives 2235; target=60  no
  85,25: 'digitsum2' gives 400; target=60  no
  52,18: '+' gives 70; target=34  no
  52,18: '-' gives 34; target=34  MATCH
  52,18: '*' gives 936; target=34  no
  52,18: 'concat' gives 5218; target=34  no
  52,18: 'rev_concat' gives 1852; target=34  no
  52,18: 'max*min+sum' gives 1006; target=34  no
  52,18: 'digitsum2' gives 256; target=34  no
The only operator consistent with all examples is '-'.
Apply to (71, 87):
  result = 16
Final: \boxed{16}


### Task: numeral
### Problem:
Convert the Roman numeral XXXIV to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  X = 10  ->  0 + 10 = 10
  X = 10  ->  10 + 10 = 20
  X = 10  ->  20 + 10 = 30
  IV = 4  ->  30 + 4 = 34
Final: \boxed{34}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  40,31 -> 4031
  52,64 -> 5264
  27,74 -> 2774
Apply to: 47,72
### Reasoning:
<|cot_start|>Examples:
  40,31 -> 4031
  52,64 -> 5264
  27,74 -> 2774
Check both candidate forms:
  concat(40,31)=4031  rev_concat(40,31)=3140  target=4031  concat
  concat(52,64)=5264  rev_concat(52,64)=6452  target=5264  concat
  concat(27,74)=2774  rev_concat(27,74)=7427  target=2774  concat
Conclude operator: concat.
Apply to (47, 72):  answer = 4772
Final: \boxed{4772}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  49,67 -> 6749
  37,60 -> 6037
  38,47 -> 4738
Apply to: 84,50
### Reasoning:
<|cot_start|>Examples:
  49,67 -> 6749
  37,60 -> 6037
  38,47 -> 4738
Check both candidate forms:
  concat(49,67)=4967  rev_concat(49,67)=6749  target=6749  rev_concat
  concat(37,60)=3760  rev_concat(37,60)=6037  target=6037  rev_concat
  concat(38,47)=3847  rev_concat(38,47)=4738  target=4738  rev_concat
Conclude operator: rev_concat.
Apply to (84, 50):  answer = 5084
Final: \boxed{5084}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11100110 -> 00000110
  10101011 -> 00001011
  10110001 -> 00000001
Apply to: 10111010
### Reasoning:
<|cot_start|>Given examples:
  11100110 -> 00000110
  10101011 -> 00001011
  10110001 -> 00000001
Compare each bit position across the three examples:
  bit 0: 1,1,1 -> 0,0,0
  bit 1: 1,0,0 -> 0,0,0
  bit 2: 1,1,1 -> 0,0,0
  bit 3: 0,0,1 -> 0,0,0
  bit 4: 0,1,0 -> 0,1,0
  bit 5: 1,0,0 -> 1,0,0
  bit 6: 1,1,0 -> 1,1,0
  bit 7: 0,1,1 -> 0,1,1
Deduce rule: and 0x0F.
Apply to 10111010:
  result = 00001010
Final: \boxed{00001010}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  33,94 -> 9433
  72,25 -> 2572
  71,41 -> 4171
Apply to: 65,33
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  33,94: '+' gives 127; target=9433  no
  33,94: '-' gives 61; target=9433  no
  33,94: '*' gives 3102; target=9433  no
  33,94: 'concat' gives 3394; target=9433  no
  33,94: 'rev_concat' gives 9433; target=9433  MATCH
  33,94: 'max*min+sum' gives 3229; target=9433  no
  33,94: 'digitsum2' gives 361; target=9433  no
  72,25: '+' gives 97; target=2572  no
  72,25: '-' gives 47; target=2572  no
  72,25: '*' gives 1800; target=2572  no
  72,25: 'concat' gives 7225; target=2572  no
  72,25: 'rev_concat' gives 2572; target=2572  MATCH
  72,25: 'max*min+sum' gives 1897; target=2572  no
  72,25: 'digitsum2' gives 256; target=2572  no
  71,41: '+' gives 112; target=4171  no
  71,41: '-' gives 30; target=4171  no
  71,41: '*' gives 2911; target=4171  no
  71,41: 'concat' gives 7141; target=4171  no
  71,41: 'rev_concat' gives 4171; target=4171  MATCH
  71,41: 'max*min+sum' gives 3023; target=4171  no
  71,41: 'digitsum2' gives 169; target=4171  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (65, 33):
  result = 3365
Final: \boxed{3365}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11010001 -> 10001011
  10111010 -> 01011101
  00110110 -> 01101100
Apply to: 00101100
### Reasoning:
<|cot_start|>Given examples:
  11010001 -> 10001011
  10111010 -> 01011101
  00110110 -> 01101100
Compare each bit position across the three examples:
  bit 0: 1,1,0 -> 1,0,0
  bit 1: 1,0,0 -> 0,1,1
  bit 2: 0,1,1 -> 0,0,1
  bit 3: 1,1,1 -> 0,1,0
  bit 4: 0,1,0 -> 1,1,1
  bit 5: 0,0,1 -> 0,1,1
  bit 6: 0,1,1 -> 1,0,0
  bit 7: 1,0,0 -> 1,1,0
Deduce rule: reverse bits.
Apply to 00101100:
  result = 00110100
Final: \boxed{00110100}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  42,35 -> 77
  75,48 -> 123
  20,23 -> 43
Apply to: 74,64
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  42,35: '+' gives 77; target=77  MATCH
  42,35: '-' gives 7; target=77  no
  42,35: '*' gives 1470; target=77  no
  42,35: 'concat' gives 4235; target=77  no
  42,35: 'rev_concat' gives 3542; target=77  no
  42,35: 'max*min+sum' gives 1547; target=77  no
  42,35: 'digitsum2' gives 196; target=77  no
  75,48: '+' gives 123; target=123  MATCH
  75,48: '-' gives 27; target=123  no
  75,48: '*' gives 3600; target=123  no
  75,48: 'concat' gives 7548; target=123  no
  75,48: 'rev_concat' gives 4875; target=123  no
  75,48: 'max*min+sum' gives 3723; target=123  no
  75,48: 'digitsum2' gives 576; target=123  no
  20,23: '+' gives 43; target=43  MATCH
  20,23: '-' gives 3; target=43  no
  20,23: '*' gives 460; target=43  no
  20,23: 'concat' gives 2023; target=43  no
  20,23: 'rev_concat' gives 2320; target=43  no
  20,23: 'max*min+sum' gives 503; target=43  no
  20,23: 'digitsum2' gives 49; target=43  no
The only operator consistent with all examples is '+'.
Apply to (74, 64):
  result = 138
Final: \boxed{138}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  50,66 -> 5066
  98,29 -> 9829
  72,42 -> 7242
Apply to: 72,53
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  50,66: '+' gives 116; target=5066  no
  50,66: '-' gives 16; target=5066  no
  50,66: '*' gives 3300; target=5066  no
  50,66: 'concat' gives 5066; target=5066  MATCH
  50,66: 'rev_concat' gives 6650; target=5066  no
  50,66: 'max*min+sum' gives 3416; target=5066  no
  50,66: 'digitsum2' gives 289; target=5066  no
  98,29: '+' gives 127; target=9829  no
  98,29: '-' gives 69; target=9829  no
  98,29: '*' gives 2842; target=9829  no
  98,29: 'concat' gives 9829; target=9829  MATCH
  98,29: 'rev_concat' gives 2998; target=9829  no
  98,29: 'max*min+sum' gives 2969; target=9829  no
  98,29: 'digitsum2' gives 784; target=9829  no
  72,42: '+' gives 114; target=7242  no
  72,42: '-' gives 30; target=7242  no
  72,42: '*' gives 3024; target=7242  no
  72,42: 'concat' gives 7242; target=7242  MATCH
  72,42: 'rev_concat' gives 4272; target=7242  no
  72,42: 'max*min+sum' gives 3138; target=7242  no
  72,42: 'digitsum2' gives 225; target=7242  no
The only operator consistent with all examples is 'concat'.
Apply to (72, 53):
  result = 7253
Final: \boxed{7253}


### Task: gravity
### Problem:
A mass of 27 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 27 * 981.
Step-by-step multiplication:
  2 * 10^1 * 981 = 19620
  running total = 19620
  7 * 10^0 * 981 = 6867
  running total = 26487
So F = 26487 centiNewtons = 264.87 N.
Final: \boxed{264.87}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  28,64 -> 2864
  36,64 -> 3664
  90,34 -> 9034
Apply to: 44,19
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  28,64: '+' gives 92; target=2864  no
  28,64: '-' gives 36; target=2864  no
  28,64: '*' gives 1792; target=2864  no
  28,64: 'concat' gives 2864; target=2864  MATCH
  28,64: 'rev_concat' gives 6428; target=2864  no
  28,64: 'max*min+sum' gives 1884; target=2864  no
  28,64: 'digitsum2' gives 400; target=2864  no
  36,64: '+' gives 100; target=3664  no
  36,64: '-' gives 28; target=3664  no
  36,64: '*' gives 2304; target=3664  no
  36,64: 'concat' gives 3664; target=3664  MATCH
  36,64: 'rev_concat' gives 6436; target=3664  no
  36,64: 'max*min+sum' gives 2404; target=3664  no
  36,64: 'digitsum2' gives 361; target=3664  no
  90,34: '+' gives 124; target=9034  no
  90,34: '-' gives 56; target=9034  no
  90,34: '*' gives 3060; target=9034  no
  90,34: 'concat' gives 9034; target=9034  MATCH
  90,34: 'rev_concat' gives 3490; target=9034  no
  90,34: 'max*min+sum' gives 3184; target=9034  no
  90,34: 'digitsum2' gives 256; target=9034  no
The only operator consistent with all examples is 'concat'.
Apply to (44, 19):
  result = 4419
Final: \boxed{4419}


### Task: gravity
### Problem:
A mass of 25 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 25 * 981.
Step-by-step multiplication:
  2 * 10^1 * 981 = 19620
  running total = 19620
  5 * 10^0 * 981 = 4905
  running total = 24525
So F = 24525 centiNewtons = 245.25 N.
Final: \boxed{245.25}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11001100 -> 01100110
  11011100 -> 01110110
  11001010 -> 01100000
Apply to: 10011010
### Reasoning:
<|cot_start|>Given examples:
  11001100 -> 01100110
  11011100 -> 01110110
  11001010 -> 01100000
Compare each bit position across the three examples:
  bit 0: 1,1,1 -> 0,0,0
  bit 1: 1,1,1 -> 1,1,1
  bit 2: 0,0,0 -> 1,1,1
  bit 3: 0,1,0 -> 0,1,0
  bit 4: 1,1,1 -> 0,0,0
  bit 5: 1,1,0 -> 1,1,0
  bit 6: 0,0,1 -> 1,1,0
  bit 7: 0,0,0 -> 0,0,0
Deduce rule: xor 0xAA.
Apply to 10011010:
  result = 00110000
Final: \boxed{00110000}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  27,86 -> 2786
  52,82 -> 5282
  31,12 -> 3112
Apply to: 15,78
### Reasoning:
<|cot_start|>Examples:
  27,86 -> 2786
  52,82 -> 5282
  31,12 -> 3112
Check both candidate forms:
  concat(27,86)=2786  rev_concat(27,86)=8627  target=2786  concat
  concat(52,82)=5282  rev_concat(52,82)=8252  target=5282  concat
  concat(31,12)=3112  rev_concat(31,12)=1231  target=3112  concat
Conclude operator: concat.
Apply to (15, 78):  answer = 1578
Final: \boxed{1578}


### Task: numeral
### Problem:
Convert the Roman numeral LVIII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  V = 5  ->  50 + 5 = 55
  I = 1  ->  55 + 1 = 56
  I = 1  ->  56 + 1 = 57
  I = 1  ->  57 + 1 = 58
Final: \boxed{58}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  91,82 -> 8291
  66,79 -> 7966
  50,86 -> 8650
Apply to: 34,81
### Reasoning:
<|cot_start|>Examples:
  91,82 -> 8291
  66,79 -> 7966
  50,86 -> 8650
Check both candidate forms:
  concat(91,82)=9182  rev_concat(91,82)=8291  target=8291  rev_concat
  concat(66,79)=6679  rev_concat(66,79)=7966  target=7966  rev_concat
  concat(50,86)=5086  rev_concat(50,86)=8650  target=8650  rev_concat
Conclude operator: rev_concat.
Apply to (34, 81):  answer = 8134
Final: \boxed{8134}


### Task: unit
### Problem:
Convert 34 litres to millilitres.
### Reasoning:
<|cot_start|>Conversion factor: 1 litres = 1000 millilitres.
So 34 litres = 34 * 1000 millilitres.
Compute step by step:
  3 * 10^1 * 1000 = 30000
  running total = 30000
  4 * 10^0 * 1000 = 4000
  running total = 34000
Final: \boxed{34000}


### Task: gravity
### Problem:
A mass of 24 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 24 * 981.
Step-by-step multiplication:
  2 * 10^1 * 981 = 19620
  running total = 19620
  4 * 10^0 * 981 = 3924
  running total = 23544
So F = 23544 centiNewtons = 235.44 N.
Final: \boxed{235.44}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  hggctvu zafb ewthnb fakkts
### Reasoning:
<|cot_start|>Cipher text: hggctvu zafb ewthnb fakkts
Try each candidate Wonderland word against each ciphertext word:
  cipher='hggctvu' candidate='alice' length-match=False
  cipher='hggctvu' candidate='rabbit' length-match=False
  cipher='hggctvu' candidate='hatter' length-match=False
  cipher='hggctvu' candidate='cheshire' length-match=False
  cipher='hggctvu' candidate='queen' length-match=False
  cipher='hggctvu' candidate='tea' length-match=False
  cipher='hggctvu' candidate='cake' length-match=False
  cipher='hggctvu' candidate='garden' length-match=False
  cipher='hggctvu' candidate='mushroom' length-match=False
  cipher='hggctvu' candidate='card' length-match=False
  cipher='hggctvu' candidate='card' length-match=False
  cipher='hggctvu' candidate='wonderland' length-match=False
  cipher='hggctvu' candidate='white' length-match=False
  cipher='hggctvu' candidate='down' length-match=False
  cipher='hggctvu' candidate='smile' length-match=False
  cipher='hggctvu' candidate='smiled' length-match=False
  cipher='hggctvu' candidate='looking' length-match=True  <- assign
  cipher='hggctvu' candidate='glass' length-match=False
  cipher='hggctvu' candidate='march' length-match=False
  cipher='hggctvu' candidate='hare' length-match=False
  cipher='hggctvu' candidate='dormouse' length-match=False
  cipher='zafb' candidate='alice' length-match=False
  cipher='zafb' candidate='rabbit' length-match=False
  cipher='zafb' candidate='hatter' length-match=False
  cipher='zafb' candidate='cheshire' length-match=False
  cipher='zafb' candidate='queen' length-match=False
  cipher='zafb' candidate='tea' length-match=False
  cipher='zafb' candidate='cake' length-match=True
  cipher='zafb' candidate='garden' length-match=False
  cipher='zafb' candidate='mushroom' length-match=False
  cipher='zafb' candidate='card' length-match=True  <- assign
  cipher='zafb' candidate='card' length-match=True  <- assign
  cipher='zafb' candidate='wonderland' length-match=False
  cipher='zafb' candidate='white' length-match=False
  cipher='zafb' candidate='down' length-match=True
  cipher='zafb' candidate='smile' length-match=False
  cipher='zafb' candidate='smiled' length-match=False
  cipher='zafb' candidate='looking' length-match=False
  cipher='zafb' candidate='glass' length-match=False
  cipher='zafb' candidate='march' length-match=False
  cipher='zafb' candidate='hare' length-match=True
  cipher='zafb' candidate='dormouse' length-match=False
  cipher='ewthnb' candidate='alice' length-match=False
  cipher='ewthnb' candidate='rabbit' length-match=True
  cipher='ewthnb' candidate='hatter' length-match=True
  cipher='ewthnb' candidate='cheshire' length-match=False
  cipher='ewthnb' candidate='queen' length-match=False
  cipher='ewthnb' candidate='tea' length-match=False
  cipher='ewthnb' candidate='cake' length-match=False
  cipher='ewthnb' candidate='garden' length-match=True
  cipher='ewthnb' candidate='mushroom' length-match=False
  cipher='ewthnb' candidate='card' length-match=False
  cipher='ewthnb' candidate='card' length-match=False
  cipher='ewthnb' candidate='wonderland' length-match=False
  cipher='ewthnb' candidate='white' length-match=False
  cipher='ewthnb' candidate='down' length-match=False
  cipher='ewthnb' candidate='smile' length-match=False
  cipher='ewthnb' candidate='smiled' length-match=True  <- assign
  cipher='ewthnb' candidate='looking' length-match=False
  cipher='ewthnb' candidate='glass' length-match=False
  cipher='ewthnb' candidate='march' length-match=False
  cipher='ewthnb' candidate='hare' length-match=False
  cipher='ewthnb' candidate='dormouse' length-match=False
  cipher='fakkts' candidate='alice' length-match=False
  cipher='fakkts' candidate='rabbit' length-match=True  <- assign
  cipher='fakkts' candidate='hatter' length-match=True
  cipher='fakkts' candidate='cheshire' length-match=False
  cipher='fakkts' candidate='queen' length-match=False
  cipher='fakkts' candidate='tea' length-match=False
  cipher='fakkts' candidate='cake' length-match=False
  cipher='fakkts' candidate='garden' length-match=True
  cipher='fakkts' candidate='mushroom' length-match=False
  cipher='fakkts' candidate='card' length-match=False
  cipher='fakkts' candidate='card' length-match=False
  cipher='fakkts' candidate='wonderland' length-match=False
  cipher='fakkts' candidate='white' length-match=False
  cipher='fakkts' candidate='down' length-match=False
  cipher='fakkts' candidate='smile' length-match=False
  cipher='fakkts' candidate='smiled' length-match=True
  cipher='fakkts' candidate='looking' length-match=False
  cipher='fakkts' candidate='glass' length-match=False
  cipher='fakkts' candidate='march' length-match=False
  cipher='fakkts' candidate='hare' length-match=False
  cipher='fakkts' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  looking card smiled rabbit
Final: \boxed{looking card smiled rabbit}


### Task: unit
### Problem:
Convert 54 litres to millilitres.
### Reasoning:
<|cot_start|>Conversion factor: 1 litres = 1000 millilitres.
So 54 litres = 54 * 1000 millilitres.
Compute step by step:
  5 * 10^1 * 1000 = 50000
  running total = 50000
  4 * 10^0 * 1000 = 4000
  running total = 54000
Final: \boxed{54000}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10110011 -> 00011001
  10100101 -> 00001111
  01100110 -> 11001100
Apply to: 00110000
### Reasoning:
<|cot_start|>Given examples:
  10110011 -> 00011001
  10100101 -> 00001111
  01100110 -> 11001100
Compare each bit position across the three examples:
  bit 0: 1,1,0 -> 0,0,1
  bit 1: 0,0,1 -> 0,0,1
  bit 2: 1,1,1 -> 0,0,0
  bit 3: 1,0,0 -> 1,0,0
  bit 4: 0,0,0 -> 1,1,1
  bit 5: 0,1,1 -> 0,1,1
  bit 6: 1,0,1 -> 0,1,0
  bit 7: 1,1,0 -> 1,1,0
Deduce rule: xor 0xAA.
Apply to 00110000:
  result = 10011010
Final: \boxed{10011010}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  jqnokbbj potwh zohnotkh pbgihkrxgi
### Reasoning:
<|cot_start|>Cipher text: jqnokbbj potwh zohnotkh pbgihkrxgi
Try each candidate Wonderland word against each ciphertext word:
  cipher='jqnokbbj' candidate='alice' length-match=False
  cipher='jqnokbbj' candidate='rabbit' length-match=False
  cipher='jqnokbbj' candidate='hatter' length-match=False
  cipher='jqnokbbj' candidate='cheshire' length-match=True
  cipher='jqnokbbj' candidate='queen' length-match=False
  cipher='jqnokbbj' candidate='tea' length-match=False
  cipher='jqnokbbj' candidate='cake' length-match=False
  cipher='jqnokbbj' candidate='garden' length-match=False
  cipher='jqnokbbj' candidate='mushroom' length-match=True  <- assign
  cipher='jqnokbbj' candidate='card' length-match=False
  cipher='jqnokbbj' candidate='card' length-match=False
  cipher='jqnokbbj' candidate='wonderland' length-match=False
  cipher='jqnokbbj' candidate='white' length-match=False
  cipher='jqnokbbj' candidate='down' length-match=False
  cipher='jqnokbbj' candidate='smile' length-match=False
  cipher='jqnokbbj' candidate='smiled' length-match=False
  cipher='jqnokbbj' candidate='looking' length-match=False
  cipher='jqnokbbj' candidate='glass' length-match=False
  cipher='jqnokbbj' candidate='march' length-match=False
  cipher='jqnokbbj' candidate='hare' length-match=False
  cipher='jqnokbbj' candidate='dormouse' length-match=True
  cipher='potwh' candidate='alice' length-match=True
  cipher='potwh' candidate='rabbit' length-match=False
  cipher='potwh' candidate='hatter' length-match=False
  cipher='potwh' candidate='cheshire' length-match=False
  cipher='potwh' candidate='queen' length-match=True
  cipher='potwh' candidate='tea' length-match=False
  cipher='potwh' candidate='cake' length-match=False
  cipher='potwh' candidate='garden' length-match=False
  cipher='potwh' candidate='mushroom' length-match=False
  cipher='potwh' candidate='card' length-match=False
  cipher='potwh' candidate='card' length-match=False
  cipher='potwh' candidate='wonderland' length-match=False
  cipher='potwh' candidate='white' length-match=True  <- assign
  cipher='potwh' candidate='down' length-match=False
  cipher='potwh' candidate='smile' length-match=True
  cipher='potwh' candidate='smiled' length-match=False
  cipher='potwh' candidate='looking' length-match=False
  cipher='potwh' candidate='glass' length-match=True
  cipher='potwh' candidate='march' length-match=True
  cipher='potwh' candidate='hare' length-match=False
  cipher='potwh' candidate='dormouse' length-match=False
  cipher='zohnotkh' candidate='alice' length-match=False
  cipher='zohnotkh' candidate='rabbit' length-match=False
  cipher='zohnotkh' candidate='hatter' length-match=False
  cipher='zohnotkh' candidate='cheshire' length-match=True  <- assign
  cipher='zohnotkh' candidate='queen' length-match=False
  cipher='zohnotkh' candidate='tea' length-match=False
  cipher='zohnotkh' candidate='cake' length-match=False
  cipher='zohnotkh' candidate='garden' length-match=False
  cipher='zohnotkh' candidate='mushroom' length-match=True
  cipher='zohnotkh' candidate='card' length-match=False
  cipher='zohnotkh' candidate='card' length-match=False
  cipher='zohnotkh' candidate='wonderland' length-match=False
  cipher='zohnotkh' candidate='white' length-match=False
  cipher='zohnotkh' candidate='down' length-match=False
  cipher='zohnotkh' candidate='smile' length-match=False
  cipher='zohnotkh' candidate='smiled' length-match=False
  cipher='zohnotkh' candidate='looking' length-match=False
  cipher='zohnotkh' candidate='glass' length-match=False
  cipher='zohnotkh' candidate='march' length-match=False
  cipher='zohnotkh' candidate='hare' length-match=False
  cipher='zohnotkh' candidate='dormouse' length-match=True
  cipher='pbgihkrxgi' candidate='alice' length-match=False
  cipher='pbgihkrxgi' candidate='rabbit' length-match=False
  cipher='pbgihkrxgi' candidate='hatter' length-match=False
  cipher='pbgihkrxgi' candidate='cheshire' length-match=False
  cipher='pbgihkrxgi' candidate='queen' length-match=False
  cipher='pbgihkrxgi' candidate='tea' length-match=False
  cipher='pbgihkrxgi' candidate='cake' length-match=False
  cipher='pbgihkrxgi' candidate='garden' length-match=False
  cipher='pbgihkrxgi' candidate='mushroom' length-match=False
  cipher='pbgihkrxgi' candidate='card' length-match=False
  cipher='pbgihkrxgi' candidate='card' length-match=False
  cipher='pbgihkrxgi' candidate='wonderland' length-match=True  <- assign
  cipher='pbgihkrxgi' candidate='white' length-match=False
  cipher='pbgihkrxgi' candidate='down' length-match=False
  cipher='pbgihkrxgi' candidate='smile' length-match=False
  cipher='pbgihkrxgi' candidate='smiled' length-match=False
  cipher='pbgihkrxgi' candidate='looking' length-match=False
  cipher='pbgihkrxgi' candidate='glass' length-match=False
  cipher='pbgihkrxgi' candidate='march' length-match=False
  cipher='pbgihkrxgi' candidate='hare' length-match=False
  cipher='pbgihkrxgi' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  mushroom white cheshire wonderland
Final: \boxed{mushroom white cheshire wonderland}


### Task: unit
### Problem:
Convert 87 kilometres to metres.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilometres = 1000 metres.
So 87 kilometres = 87 * 1000 metres.
Compute step by step:
  8 * 10^1 * 1000 = 80000
  running total = 80000
  7 * 10^0 * 1000 = 7000
  running total = 87000
Final: \boxed{87000}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  42,79 -> 7942
  54,29 -> 2954
  15,11 -> 1115
Apply to: 26,59
### Reasoning:
<|cot_start|>Examples:
  42,79 -> 7942
  54,29 -> 2954
  15,11 -> 1115
Check both candidate forms:
  concat(42,79)=4279  rev_concat(42,79)=7942  target=7942  rev_concat
  concat(54,29)=5429  rev_concat(54,29)=2954  target=2954  rev_concat
  concat(15,11)=1511  rev_concat(15,11)=1115  target=1115  rev_concat
Conclude operator: rev_concat.
Apply to (26, 59):  answer = 5926
Final: \boxed{5926}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  76,16 -> 1676
  68,83 -> 8368
  82,41 -> 4182
Apply to: 60,43
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  76,16: '+' gives 92; target=1676  no
  76,16: '-' gives 60; target=1676  no
  76,16: '*' gives 1216; target=1676  no
  76,16: 'concat' gives 7616; target=1676  no
  76,16: 'rev_concat' gives 1676; target=1676  MATCH
  76,16: 'max*min+sum' gives 1308; target=1676  no
  76,16: 'digitsum2' gives 400; target=1676  no
  68,83: '+' gives 151; target=8368  no
  68,83: '-' gives 15; target=8368  no
  68,83: '*' gives 5644; target=8368  no
  68,83: 'concat' gives 6883; target=8368  no
  68,83: 'rev_concat' gives 8368; target=8368  MATCH
  68,83: 'max*min+sum' gives 5795; target=8368  no
  68,83: 'digitsum2' gives 625; target=8368  no
  82,41: '+' gives 123; target=4182  no
  82,41: '-' gives 41; target=4182  no
  82,41: '*' gives 3362; target=4182  no
  82,41: 'concat' gives 8241; target=4182  no
  82,41: 'rev_concat' gives 4182; target=4182  MATCH
  82,41: 'max*min+sum' gives 3485; target=4182  no
  82,41: 'digitsum2' gives 225; target=4182  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (60, 43):
  result = 4360
Final: \boxed{4360}


### Task: gravity
### Problem:
A mass of 39 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 39 * 981.
Step-by-step multiplication:
  3 * 10^1 * 981 = 29430
  running total = 29430
  9 * 10^0 * 981 = 8829
  running total = 38259
So F = 38259 centiNewtons = 382.59 N.
Final: \boxed{382.59}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  nrz yzbgro ytzxx fmrro
### Reasoning:
<|cot_start|>Cipher text: nrz yzbgro ytzxx fmrro
Try each candidate Wonderland word against each ciphertext word:
  cipher='nrz' candidate='alice' length-match=False
  cipher='nrz' candidate='rabbit' length-match=False
  cipher='nrz' candidate='hatter' length-match=False
  cipher='nrz' candidate='cheshire' length-match=False
  cipher='nrz' candidate='queen' length-match=False
  cipher='nrz' candidate='tea' length-match=True  <- assign
  cipher='nrz' candidate='cake' length-match=False
  cipher='nrz' candidate='garden' length-match=False
  cipher='nrz' candidate='mushroom' length-match=False
  cipher='nrz' candidate='card' length-match=False
  cipher='nrz' candidate='card' length-match=False
  cipher='nrz' candidate='wonderland' length-match=False
  cipher='nrz' candidate='white' length-match=False
  cipher='nrz' candidate='down' length-match=False
  cipher='nrz' candidate='smile' length-match=False
  cipher='nrz' candidate='smiled' length-match=False
  cipher='nrz' candidate='looking' length-match=False
  cipher='nrz' candidate='glass' length-match=False
  cipher='nrz' candidate='march' length-match=False
  cipher='nrz' candidate='hare' length-match=False
  cipher='nrz' candidate='dormouse' length-match=False
  cipher='yzbgro' candidate='alice' length-match=False
  cipher='yzbgro' candidate='rabbit' length-match=True
  cipher='yzbgro' candidate='hatter' length-match=True
  cipher='yzbgro' candidate='cheshire' length-match=False
  cipher='yzbgro' candidate='queen' length-match=False
  cipher='yzbgro' candidate='tea' length-match=False
  cipher='yzbgro' candidate='cake' length-match=False
  cipher='yzbgro' candidate='garden' length-match=True  <- assign
  cipher='yzbgro' candidate='mushroom' length-match=False
  cipher='yzbgro' candidate='card' length-match=False
  cipher='yzbgro' candidate='card' length-match=False
  cipher='yzbgro' candidate='wonderland' length-match=False
  cipher='yzbgro' candidate='white' length-match=False
  cipher='yzbgro' candidate='down' length-match=False
  cipher='yzbgro' candidate='smile' length-match=False
  cipher='yzbgro' candidate='smiled' length-match=True
  cipher='yzbgro' candidate='looking' length-match=False
  cipher='yzbgro' candidate='glass' length-match=False
  cipher='yzbgro' candidate='march' length-match=False
  cipher='yzbgro' candidate='hare' length-match=False
  cipher='yzbgro' candidate='dormouse' length-match=False
  cipher='ytzxx' candidate='alice' length-match=True
  cipher='ytzxx' candidate='rabbit' length-match=False
  cipher='ytzxx' candidate='hatter' length-match=False
  cipher='ytzxx' candidate='cheshire' length-match=False
  cipher='ytzxx' candidate='queen' length-match=True
  cipher='ytzxx' candidate='tea' length-match=False
  cipher='ytzxx' candidate='cake' length-match=False
  cipher='ytzxx' candidate='garden' length-match=False
  cipher='ytzxx' candidate='mushroom' length-match=False
  cipher='ytzxx' candidate='card' length-match=False
  cipher='ytzxx' candidate='card' length-match=False
  cipher='ytzxx' candidate='wonderland' length-match=False
  cipher='ytzxx' candidate='white' length-match=True
  cipher='ytzxx' candidate='down' length-match=False
  cipher='ytzxx' candidate='smile' length-match=True
  cipher='ytzxx' candidate='smiled' length-match=False
  cipher='ytzxx' candidate='looking' length-match=False
  cipher='ytzxx' candidate='glass' length-match=True  <- assign
  cipher='ytzxx' candidate='march' length-match=True
  cipher='ytzxx' candidate='hare' length-match=False
  cipher='ytzxx' candidate='dormouse' length-match=False
  cipher='fmrro' candidate='alice' length-match=True
  cipher='fmrro' candidate='rabbit' length-match=False
  cipher='fmrro' candidate='hatter' length-match=False
  cipher='fmrro' candidate='cheshire' length-match=False
  cipher='fmrro' candidate='queen' length-match=True  <- assign
  cipher='fmrro' candidate='tea' length-match=False
  cipher='fmrro' candidate='cake' length-match=False
  cipher='fmrro' candidate='garden' length-match=False
  cipher='fmrro' candidate='mushroom' length-match=False
  cipher='fmrro' candidate='card' length-match=False
  cipher='fmrro' candidate='card' length-match=False
  cipher='fmrro' candidate='wonderland' length-match=False
  cipher='fmrro' candidate='white' length-match=True
  cipher='fmrro' candidate='down' length-match=False
  cipher='fmrro' candidate='smile' length-match=True
  cipher='fmrro' candidate='smiled' length-match=False
  cipher='fmrro' candidate='looking' length-match=False
  cipher='fmrro' candidate='glass' length-match=True
  cipher='fmrro' candidate='march' length-match=True
  cipher='fmrro' candidate='hare' length-match=False
  cipher='fmrro' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  tea garden glass queen
Final: \boxed{tea garden glass queen}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10010001 -> 00011001
  10110100 -> 01001011
  10111111 -> 11111011
Apply to: 00001010
### Reasoning:
<|cot_start|>Given examples:
  10010001 -> 00011001
  10110100 -> 01001011
  10111111 -> 11111011
Compare each bit position across the three examples:
  bit 0: 1,1,1 -> 0,0,1
  bit 1: 0,0,0 -> 0,1,1
  bit 2: 0,1,1 -> 0,0,1
  bit 3: 1,1,1 -> 1,0,1
  bit 4: 0,0,1 -> 1,1,1
  bit 5: 0,1,1 -> 0,0,0
  bit 6: 0,0,1 -> 0,1,1
  bit 7: 1,0,1 -> 1,1,1
Deduce rule: swap nibbles.
Apply to 00001010:
  result = 10100000
Final: \boxed{10100000}


### Task: numeral
### Problem:
Convert the Roman numeral LXXVII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  X = 10  ->  50 + 10 = 60
  X = 10  ->  60 + 10 = 70
  V = 5  ->  70 + 5 = 75
  I = 1  ->  75 + 1 = 76
  I = 1  ->  76 + 1 = 77
Final: \boxed{77}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  cbzzl jazuaxvz jgtz agsszv
### Reasoning:
<|cot_start|>Cipher text: cbzzl jazuaxvz jgtz agsszv
Try each candidate Wonderland word against each ciphertext word:
  cipher='cbzzl' candidate='alice' length-match=True
  cipher='cbzzl' candidate='rabbit' length-match=False
  cipher='cbzzl' candidate='hatter' length-match=False
  cipher='cbzzl' candidate='cheshire' length-match=False
  cipher='cbzzl' candidate='queen' length-match=True  <- assign
  cipher='cbzzl' candidate='tea' length-match=False
  cipher='cbzzl' candidate='cake' length-match=False
  cipher='cbzzl' candidate='garden' length-match=False
  cipher='cbzzl' candidate='mushroom' length-match=False
  cipher='cbzzl' candidate='card' length-match=False
  cipher='cbzzl' candidate='card' length-match=False
  cipher='cbzzl' candidate='wonderland' length-match=False
  cipher='cbzzl' candidate='white' length-match=True
  cipher='cbzzl' candidate='down' length-match=False
  cipher='cbzzl' candidate='smile' length-match=True
  cipher='cbzzl' candidate='smiled' length-match=False
  cipher='cbzzl' candidate='looking' length-match=False
  cipher='cbzzl' candidate='glass' length-match=True
  cipher='cbzzl' candidate='march' length-match=True
  cipher='cbzzl' candidate='hare' length-match=False
  cipher='cbzzl' candidate='dormouse' length-match=False
  cipher='jazuaxvz' candidate='alice' length-match=False
  cipher='jazuaxvz' candidate='rabbit' length-match=False
  cipher='jazuaxvz' candidate='hatter' length-match=False
  cipher='jazuaxvz' candidate='cheshire' length-match=True  <- assign
  cipher='jazuaxvz' candidate='queen' length-match=False
  cipher='jazuaxvz' candidate='tea' length-match=False
  cipher='jazuaxvz' candidate='cake' length-match=False
  cipher='jazuaxvz' candidate='garden' length-match=False
  cipher='jazuaxvz' candidate='mushroom' length-match=True
  cipher='jazuaxvz' candidate='card' length-match=False
  cipher='jazuaxvz' candidate='card' length-match=False
  cipher='jazuaxvz' candidate='wonderland' length-match=False
  cipher='jazuaxvz' candidate='white' length-match=False
  cipher='jazuaxvz' candidate='down' length-match=False
  cipher='jazuaxvz' candidate='smile' length-match=False
  cipher='jazuaxvz' candidate='smiled' length-match=False
  cipher='jazuaxvz' candidate='looking' length-match=False
  cipher='jazuaxvz' candidate='glass' length-match=False
  cipher='jazuaxvz' candidate='march' length-match=False
  cipher='jazuaxvz' candidate='hare' length-match=False
  cipher='jazuaxvz' candidate='dormouse' length-match=True
  cipher='jgtz' candidate='alice' length-match=False
  cipher='jgtz' candidate='rabbit' length-match=False
  cipher='jgtz' candidate='hatter' length-match=False
  cipher='jgtz' candidate='cheshire' length-match=False
  cipher='jgtz' candidate='queen' length-match=False
  cipher='jgtz' candidate='tea' length-match=False
  cipher='jgtz' candidate='cake' length-match=True  <- assign
  cipher='jgtz' candidate='garden' length-match=False
  cipher='jgtz' candidate='mushroom' length-match=False
  cipher='jgtz' candidate='card' length-match=True
  cipher='jgtz' candidate='card' length-match=True
  cipher='jgtz' candidate='wonderland' length-match=False
  cipher='jgtz' candidate='white' length-match=False
  cipher='jgtz' candidate='down' length-match=True
  cipher='jgtz' candidate='smile' length-match=False
  cipher='jgtz' candidate='smiled' length-match=False
  cipher='jgtz' candidate='looking' length-match=False
  cipher='jgtz' candidate='glass' length-match=False
  cipher='jgtz' candidate='march' length-match=False
  cipher='jgtz' candidate='hare' length-match=True
  cipher='jgtz' candidate='dormouse' length-match=False
  cipher='agsszv' candidate='alice' length-match=False
  cipher='agsszv' candidate='rabbit' length-match=True
  cipher='agsszv' candidate='hatter' length-match=True  <- assign
  cipher='agsszv' candidate='cheshire' length-match=False
  cipher='agsszv' candidate='queen' length-match=False
  cipher='agsszv' candidate='tea' length-match=False
  cipher='agsszv' candidate='cake' length-match=False
  cipher='agsszv' candidate='garden' length-match=True
  cipher='agsszv' candidate='mushroom' length-match=False
  cipher='agsszv' candidate='card' length-match=False
  cipher='agsszv' candidate='card' length-match=False
  cipher='agsszv' candidate='wonderland' length-match=False
  cipher='agsszv' candidate='white' length-match=False
  cipher='agsszv' candidate='down' length-match=False
  cipher='agsszv' candidate='smile' length-match=False
  cipher='agsszv' candidate='smiled' length-match=True
  cipher='agsszv' candidate='looking' length-match=False
  cipher='agsszv' candidate='glass' length-match=False
  cipher='agsszv' candidate='march' length-match=False
  cipher='agsszv' candidate='hare' length-match=False
  cipher='agsszv' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  queen cheshire cake hatter
Final: \boxed{queen cheshire cake hatter}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  66,62 -> 6266
  82,22 -> 2282
  16,59 -> 5916
Apply to: 47,89
### Reasoning:
<|cot_start|>Examples:
  66,62 -> 6266
  82,22 -> 2282
  16,59 -> 5916
Check both candidate forms:
  concat(66,62)=6662  rev_concat(66,62)=6266  target=6266  rev_concat
  concat(82,22)=8222  rev_concat(82,22)=2282  target=2282  rev_concat
  concat(16,59)=1659  rev_concat(16,59)=5916  target=5916  rev_concat
Conclude operator: rev_concat.
Apply to (47, 89):  answer = 8947
Final: \boxed{8947}


### Task: unit
### Problem:
Convert 36 minutes to seconds.
### Reasoning:
<|cot_start|>Conversion factor: 1 minutes = 60 seconds.
So 36 minutes = 36 * 60 seconds.
Compute step by step:
  3 * 10^1 * 60 = 1800
  running total = 1800
  6 * 10^0 * 60 = 360
  running total = 2160
Final: \boxed{2160}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  dmmwojt nxiy txiyzj pzx
### Reasoning:
<|cot_start|>Cipher text: dmmwojt nxiy txiyzj pzx
Try each candidate Wonderland word against each ciphertext word:
  cipher='dmmwojt' candidate='alice' length-match=False
  cipher='dmmwojt' candidate='rabbit' length-match=False
  cipher='dmmwojt' candidate='hatter' length-match=False
  cipher='dmmwojt' candidate='cheshire' length-match=False
  cipher='dmmwojt' candidate='queen' length-match=False
  cipher='dmmwojt' candidate='tea' length-match=False
  cipher='dmmwojt' candidate='cake' length-match=False
  cipher='dmmwojt' candidate='garden' length-match=False
  cipher='dmmwojt' candidate='mushroom' length-match=False
  cipher='dmmwojt' candidate='card' length-match=False
  cipher='dmmwojt' candidate='card' length-match=False
  cipher='dmmwojt' candidate='wonderland' length-match=False
  cipher='dmmwojt' candidate='white' length-match=False
  cipher='dmmwojt' candidate='down' length-match=False
  cipher='dmmwojt' candidate='smile' length-match=False
  cipher='dmmwojt' candidate='smiled' length-match=False
  cipher='dmmwojt' candidate='looking' length-match=True  <- assign
  cipher='dmmwojt' candidate='glass' length-match=False
  cipher='dmmwojt' candidate='march' length-match=False
  cipher='dmmwojt' candidate='hare' length-match=False
  cipher='dmmwojt' candidate='dormouse' length-match=False
  cipher='nxiy' candidate='alice' length-match=False
  cipher='nxiy' candidate='rabbit' length-match=False
  cipher='nxiy' candidate='hatter' length-match=False
  cipher='nxiy' candidate='cheshire' length-match=False
  cipher='nxiy' candidate='queen' length-match=False
  cipher='nxiy' candidate='tea' length-match=False
  cipher='nxiy' candidate='cake' length-match=True
  cipher='nxiy' candidate='garden' length-match=False
  cipher='nxiy' candidate='mushroom' length-match=False
  cipher='nxiy' candidate='card' length-match=True  <- assign
  cipher='nxiy' candidate='card' length-match=True  <- assign
  cipher='nxiy' candidate='wonderland' length-match=False
  cipher='nxiy' candidate='white' length-match=False
  cipher='nxiy' candidate='down' length-match=True
  cipher='nxiy' candidate='smile' length-match=False
  cipher='nxiy' candidate='smiled' length-match=False
  cipher='nxiy' candidate='looking' length-match=False
  cipher='nxiy' candidate='glass' length-match=False
  cipher='nxiy' candidate='march' length-match=False
  cipher='nxiy' candidate='hare' length-match=True
  cipher='nxiy' candidate='dormouse' length-match=False
  cipher='txiyzj' candidate='alice' length-match=False
  cipher='txiyzj' candidate='rabbit' length-match=True
  cipher='txiyzj' candidate='hatter' length-match=True
  cipher='txiyzj' candidate='cheshire' length-match=False
  cipher='txiyzj' candidate='queen' length-match=False
  cipher='txiyzj' candidate='tea' length-match=False
  cipher='txiyzj' candidate='cake' length-match=False
  cipher='txiyzj' candidate='garden' length-match=True  <- assign
  cipher='txiyzj' candidate='mushroom' length-match=False
  cipher='txiyzj' candidate='card' length-match=False
  cipher='txiyzj' candidate='card' length-match=False
  cipher='txiyzj' candidate='wonderland' length-match=False
  cipher='txiyzj' candidate='white' length-match=False
  cipher='txiyzj' candidate='down' length-match=False
  cipher='txiyzj' candidate='smile' length-match=False
  cipher='txiyzj' candidate='smiled' length-match=True
  cipher='txiyzj' candidate='looking' length-match=False
  cipher='txiyzj' candidate='glass' length-match=False
  cipher='txiyzj' candidate='march' length-match=False
  cipher='txiyzj' candidate='hare' length-match=False
  cipher='txiyzj' candidate='dormouse' length-match=False
  cipher='pzx' candidate='alice' length-match=False
  cipher='pzx' candidate='rabbit' length-match=False
  cipher='pzx' candidate='hatter' length-match=False
  cipher='pzx' candidate='cheshire' length-match=False
  cipher='pzx' candidate='queen' length-match=False
  cipher='pzx' candidate='tea' length-match=True  <- assign
  cipher='pzx' candidate='cake' length-match=False
  cipher='pzx' candidate='garden' length-match=False
  cipher='pzx' candidate='mushroom' length-match=False
  cipher='pzx' candidate='card' length-match=False
  cipher='pzx' candidate='card' length-match=False
  cipher='pzx' candidate='wonderland' length-match=False
  cipher='pzx' candidate='white' length-match=False
  cipher='pzx' candidate='down' length-match=False
  cipher='pzx' candidate='smile' length-match=False
  cipher='pzx' candidate='smiled' length-match=False
  cipher='pzx' candidate='looking' length-match=False
  cipher='pzx' candidate='glass' length-match=False
  cipher='pzx' candidate='march' length-match=False
  cipher='pzx' candidate='hare' length-match=False
  cipher='pzx' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  looking card garden tea
Final: \boxed{looking card garden tea}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11110001 -> 11110001
  11100011 -> 11110011
  11110011 -> 11110011
Apply to: 01011110
### Reasoning:
<|cot_start|>Given examples:
  11110001 -> 11110001
  11100011 -> 11110011
  11110011 -> 11110011
Compare each bit position across the three examples:
  bit 0: 1,1,1 -> 1,1,1
  bit 1: 1,1,1 -> 1,1,1
  bit 2: 1,1,1 -> 1,1,1
  bit 3: 1,0,1 -> 1,1,1
  bit 4: 0,0,0 -> 0,0,0
  bit 5: 0,0,0 -> 0,0,0
  bit 6: 0,1,1 -> 0,1,1
  bit 7: 1,1,1 -> 1,1,1
Deduce rule: or 0xF0.
Apply to 01011110:
  result = 11111110
Final: \boxed{11111110}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  ayyxhdg nyvryjcz vuwwhp fuppzv
### Reasoning:
<|cot_start|>Cipher text: ayyxhdg nyvryjcz vuwwhp fuppzv
Try each candidate Wonderland word against each ciphertext word:
  cipher='ayyxhdg' candidate='alice' length-match=False
  cipher='ayyxhdg' candidate='rabbit' length-match=False
  cipher='ayyxhdg' candidate='hatter' length-match=False
  cipher='ayyxhdg' candidate='cheshire' length-match=False
  cipher='ayyxhdg' candidate='queen' length-match=False
  cipher='ayyxhdg' candidate='tea' length-match=False
  cipher='ayyxhdg' candidate='cake' length-match=False
  cipher='ayyxhdg' candidate='garden' length-match=False
  cipher='ayyxhdg' candidate='mushroom' length-match=False
  cipher='ayyxhdg' candidate='card' length-match=False
  cipher='ayyxhdg' candidate='card' length-match=False
  cipher='ayyxhdg' candidate='wonderland' length-match=False
  cipher='ayyxhdg' candidate='white' length-match=False
  cipher='ayyxhdg' candidate='down' length-match=False
  cipher='ayyxhdg' candidate='smile' length-match=False
  cipher='ayyxhdg' candidate='smiled' length-match=False
  cipher='ayyxhdg' candidate='looking' length-match=True  <- assign
  cipher='ayyxhdg' candidate='glass' length-match=False
  cipher='ayyxhdg' candidate='march' length-match=False
  cipher='ayyxhdg' candidate='hare' length-match=False
  cipher='ayyxhdg' candidate='dormouse' length-match=False
  cipher='nyvryjcz' candidate='alice' length-match=False
  cipher='nyvryjcz' candidate='rabbit' length-match=False
  cipher='nyvryjcz' candidate='hatter' length-match=False
  cipher='nyvryjcz' candidate='cheshire' length-match=True
  cipher='nyvryjcz' candidate='queen' length-match=False
  cipher='nyvryjcz' candidate='tea' length-match=False
  cipher='nyvryjcz' candidate='cake' length-match=False
  cipher='nyvryjcz' candidate='garden' length-match=False
  cipher='nyvryjcz' candidate='mushroom' length-match=True
  cipher='nyvryjcz' candidate='card' length-match=False
  cipher='nyvryjcz' candidate='card' length-match=False
  cipher='nyvryjcz' candidate='wonderland' length-match=False
  cipher='nyvryjcz' candidate='white' length-match=False
  cipher='nyvryjcz' candidate='down' length-match=False
  cipher='nyvryjcz' candidate='smile' length-match=False
  cipher='nyvryjcz' candidate='smiled' length-match=False
  cipher='nyvryjcz' candidate='looking' length-match=False
  cipher='nyvryjcz' candidate='glass' length-match=False
  cipher='nyvryjcz' candidate='march' length-match=False
  cipher='nyvryjcz' candidate='hare' length-match=False
  cipher='nyvryjcz' candidate='dormouse' length-match=True  <- assign
  cipher='vuwwhp' candidate='alice' length-match=False
  cipher='vuwwhp' candidate='rabbit' length-match=True  <- assign
  cipher='vuwwhp' candidate='hatter' length-match=True
  cipher='vuwwhp' candidate='cheshire' length-match=False
  cipher='vuwwhp' candidate='queen' length-match=False
  cipher='vuwwhp' candidate='tea' length-match=False
  cipher='vuwwhp' candidate='cake' length-match=False
  cipher='vuwwhp' candidate='garden' length-match=True
  cipher='vuwwhp' candidate='mushroom' length-match=False
  cipher='vuwwhp' candidate='card' length-match=False
  cipher='vuwwhp' candidate='card' length-match=False
  cipher='vuwwhp' candidate='wonderland' length-match=False
  cipher='vuwwhp' candidate='white' length-match=False
  cipher='vuwwhp' candidate='down' length-match=False
  cipher='vuwwhp' candidate='smile' length-match=False
  cipher='vuwwhp' candidate='smiled' length-match=True
  cipher='vuwwhp' candidate='looking' length-match=False
  cipher='vuwwhp' candidate='glass' length-match=False
  cipher='vuwwhp' candidate='march' length-match=False
  cipher='vuwwhp' candidate='hare' length-match=False
  cipher='vuwwhp' candidate='dormouse' length-match=False
  cipher='fuppzv' candidate='alice' length-match=False
  cipher='fuppzv' candidate='rabbit' length-match=True
  cipher='fuppzv' candidate='hatter' length-match=True  <- assign
  cipher='fuppzv' candidate='cheshire' length-match=False
  cipher='fuppzv' candidate='queen' length-match=False
  cipher='fuppzv' candidate='tea' length-match=False
  cipher='fuppzv' candidate='cake' length-match=False
  cipher='fuppzv' candidate='garden' length-match=True
  cipher='fuppzv' candidate='mushroom' length-match=False
  cipher='fuppzv' candidate='card' length-match=False
  cipher='fuppzv' candidate='card' length-match=False
  cipher='fuppzv' candidate='wonderland' length-match=False
  cipher='fuppzv' candidate='white' length-match=False
  cipher='fuppzv' candidate='down' length-match=False
  cipher='fuppzv' candidate='smile' length-match=False
  cipher='fuppzv' candidate='smiled' length-match=True
  cipher='fuppzv' candidate='looking' length-match=False
  cipher='fuppzv' candidate='glass' length-match=False
  cipher='fuppzv' candidate='march' length-match=False
  cipher='fuppzv' candidate='hare' length-match=False
  cipher='fuppzv' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  looking dormouse rabbit hatter
Final: \boxed{looking dormouse rabbit hatter}


### Task: gravity
### Problem:
A mass of 37 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 37 * 981.
Step-by-step multiplication:
  3 * 10^1 * 981 = 29430
  running total = 29430
  7 * 10^0 * 981 = 6867
  running total = 36297
So F = 36297 centiNewtons = 362.97 N.
Final: \boxed{362.97}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  94,12 -> 256
  52,29 -> 324
  23,75 -> 289
Apply to: 50,87
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  94,12: '+' gives 106; target=256  no
  94,12: '-' gives 82; target=256  no
  94,12: '*' gives 1128; target=256  no
  94,12: 'concat' gives 9412; target=256  no
  94,12: 'rev_concat' gives 1294; target=256  no
  94,12: 'max*min+sum' gives 1234; target=256  no
  94,12: 'digitsum2' gives 256; target=256  MATCH
  52,29: '+' gives 81; target=324  no
  52,29: '-' gives 23; target=324  no
  52,29: '*' gives 1508; target=324  no
  52,29: 'concat' gives 5229; target=324  no
  52,29: 'rev_concat' gives 2952; target=324  no
  52,29: 'max*min+sum' gives 1589; target=324  no
  52,29: 'digitsum2' gives 324; target=324  MATCH
  23,75: '+' gives 98; target=289  no
  23,75: '-' gives 52; target=289  no
  23,75: '*' gives 1725; target=289  no
  23,75: 'concat' gives 2375; target=289  no
  23,75: 'rev_concat' gives 7523; target=289  no
  23,75: 'max*min+sum' gives 1823; target=289  no
  23,75: 'digitsum2' gives 289; target=289  MATCH
The only operator consistent with all examples is 'digitsum2'.
Apply to (50, 87):
  result = 400
Final: \boxed{400}


### Task: numeral
### Problem:
Convert the Roman numeral VIII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  V = 5  ->  0 + 5 = 5
  I = 1  ->  5 + 1 = 6
  I = 1  ->  6 + 1 = 7
  I = 1  ->  7 + 1 = 8
Final: \boxed{8}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  xkkishw mlnba uastv emsxv
### Reasoning:
<|cot_start|>Cipher text: xkkishw mlnba uastv emsxv
Try each candidate Wonderland word against each ciphertext word:
  cipher='xkkishw' candidate='alice' length-match=False
  cipher='xkkishw' candidate='rabbit' length-match=False
  cipher='xkkishw' candidate='hatter' length-match=False
  cipher='xkkishw' candidate='cheshire' length-match=False
  cipher='xkkishw' candidate='queen' length-match=False
  cipher='xkkishw' candidate='tea' length-match=False
  cipher='xkkishw' candidate='cake' length-match=False
  cipher='xkkishw' candidate='garden' length-match=False
  cipher='xkkishw' candidate='mushroom' length-match=False
  cipher='xkkishw' candidate='card' length-match=False
  cipher='xkkishw' candidate='card' length-match=False
  cipher='xkkishw' candidate='wonderland' length-match=False
  cipher='xkkishw' candidate='white' length-match=False
  cipher='xkkishw' candidate='down' length-match=False
  cipher='xkkishw' candidate='smile' length-match=False
  cipher='xkkishw' candidate='smiled' length-match=False
  cipher='xkkishw' candidate='looking' length-match=True  <- assign
  cipher='xkkishw' candidate='glass' length-match=False
  cipher='xkkishw' candidate='march' length-match=False
  cipher='xkkishw' candidate='hare' length-match=False
  cipher='xkkishw' candidate='dormouse' length-match=False
  cipher='mlnba' candidate='alice' length-match=True
  cipher='mlnba' candidate='rabbit' length-match=False
  cipher='mlnba' candidate='hatter' length-match=False
  cipher='mlnba' candidate='cheshire' length-match=False
  cipher='mlnba' candidate='queen' length-match=True
  cipher='mlnba' candidate='tea' length-match=False
  cipher='mlnba' candidate='cake' length-match=False
  cipher='mlnba' candidate='garden' length-match=False
  cipher='mlnba' candidate='mushroom' length-match=False
  cipher='mlnba' candidate='card' length-match=False
  cipher='mlnba' candidate='card' length-match=False
  cipher='mlnba' candidate='wonderland' length-match=False
  cipher='mlnba' candidate='white' length-match=True
  cipher='mlnba' candidate='down' length-match=False
  cipher='mlnba' candidate='smile' length-match=True
  cipher='mlnba' candidate='smiled' length-match=False
  cipher='mlnba' candidate='looking' length-match=False
  cipher='mlnba' candidate='glass' length-match=True
  cipher='mlnba' candidate='march' length-match=True  <- assign
  cipher='mlnba' candidate='hare' length-match=False
  cipher='mlnba' candidate='dormouse' length-match=False
  cipher='uastv' candidate='alice' length-match=True
  cipher='uastv' candidate='rabbit' length-match=False
  cipher='uastv' candidate='hatter' length-match=False
  cipher='uastv' candidate='cheshire' length-match=False
  cipher='uastv' candidate='queen' length-match=True
  cipher='uastv' candidate='tea' length-match=False
  cipher='uastv' candidate='cake' length-match=False
  cipher='uastv' candidate='garden' length-match=False
  cipher='uastv' candidate='mushroom' length-match=False
  cipher='uastv' candidate='card' length-match=False
  cipher='uastv' candidate='card' length-match=False
  cipher='uastv' candidate='wonderland' length-match=False
  cipher='uastv' candidate='white' length-match=True  <- assign
  cipher='uastv' candidate='down' length-match=False
  cipher='uastv' candidate='smile' length-match=True
  cipher='uastv' candidate='smiled' length-match=False
  cipher='uastv' candidate='looking' length-match=False
  cipher='uastv' candidate='glass' length-match=True
  cipher='uastv' candidate='march' length-match=True
  cipher='uastv' candidate='hare' length-match=False
  cipher='uastv' candidate='dormouse' length-match=False
  cipher='emsxv' candidate='alice' length-match=True
  cipher='emsxv' candidate='rabbit' length-match=False
  cipher='emsxv' candidate='hatter' length-match=False
  cipher='emsxv' candidate='cheshire' length-match=False
  cipher='emsxv' candidate='queen' length-match=True
  cipher='emsxv' candidate='tea' length-match=False
  cipher='emsxv' candidate='cake' length-match=False
  cipher='emsxv' candidate='garden' length-match=False
  cipher='emsxv' candidate='mushroom' length-match=False
  cipher='emsxv' candidate='card' length-match=False
  cipher='emsxv' candidate='card' length-match=False
  cipher='emsxv' candidate='wonderland' length-match=False
  cipher='emsxv' candidate='white' length-match=True
  cipher='emsxv' candidate='down' length-match=False
  cipher='emsxv' candidate='smile' length-match=True  <- assign
  cipher='emsxv' candidate='smiled' length-match=False
  cipher='emsxv' candidate='looking' length-match=False
  cipher='emsxv' candidate='glass' length-match=True
  cipher='emsxv' candidate='march' length-match=True
  cipher='emsxv' candidate='hare' length-match=False
  cipher='emsxv' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  looking march white smile
Final: \boxed{looking march white smile}


### Task: gravity
### Problem:
A mass of 21 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 21 * 981.
Step-by-step multiplication:
  2 * 10^1 * 981 = 19620
  running total = 19620
  1 * 10^0 * 981 = 981
  running total = 20601
So F = 20601 centiNewtons = 206.01 N.
Final: \boxed{206.01}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  61,61 -> 6161
  17,49 -> 1749
  32,31 -> 3231
Apply to: 51,25
### Reasoning:
<|cot_start|>Examples:
  61,61 -> 6161
  17,49 -> 1749
  32,31 -> 3231
Check both candidate forms:
  concat(61,61)=6161  rev_concat(61,61)=6161  target=6161  concat
  concat(17,49)=1749  rev_concat(17,49)=4917  target=1749  concat
  concat(32,31)=3231  rev_concat(32,31)=3132  target=3231  concat
Conclude operator: concat.
Apply to (51, 25):  answer = 5125
Final: \boxed{5125}


### Task: unit
### Problem:
Convert 8 days to hours.
### Reasoning:
<|cot_start|>Conversion factor: 1 days = 24 hours.
So 8 days = 8 * 24 hours.
Compute step by step:
  8 * 10^0 * 24 = 192
  running total = 192
Final: \boxed{192}


### Task: numeral
### Problem:
Convert the Roman numeral X to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  X = 10  ->  0 + 10 = 10
Final: \boxed{10}