### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  13,57 -> 1357
  52,76 -> 5276
  85,85 -> 8585
Apply to: 61,79
### Reasoning:
<|cot_start|>Examples:
  13,57 -> 1357
  52,76 -> 5276
  85,85 -> 8585
Check both candidate forms:
  concat(13,57)=1357  rev_concat(13,57)=5713  target=1357  concat
  concat(52,76)=5276  rev_concat(52,76)=7652  target=5276  concat
  concat(85,85)=8585  rev_concat(85,85)=8585  target=8585  concat
Conclude operator: concat.
Apply to (61, 79):  answer = 6179
Final: \boxed{6179}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11101111 -> 00001111
  10000001 -> 00000001
  10110000 -> 00000000
Apply to: 10001011
### Reasoning:
<|cot_start|>Given examples:
  11101111 -> 00001111
  10000001 -> 00000001
  10110000 -> 00000000
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: 1,0,1 -> 0,0,0
  bit 3: 0,0,1 -> 0,0,0
  bit 4: 1,0,0 -> 1,0,0
  bit 5: 1,0,0 -> 1,0,0
  bit 6: 1,0,0 -> 1,0,0
  bit 7: 1,1,0 -> 1,1,0
Deduce rule: and 0x0F.
Apply to 10001011:
  result = 00001011
Final: \boxed{00001011}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00001101 -> 00001101
  11000101 -> 00000101
  11100101 -> 00000101
Apply to: 00011010
### Reasoning:
<|cot_start|>Given examples:
  00001101 -> 00001101
  11000101 -> 00000101
  11100101 -> 00000101
Compare each bit position across the three examples:
  bit 0: 0,1,1 -> 0,0,0
  bit 1: 0,1,1 -> 0,0,0
  bit 2: 0,0,1 -> 0,0,0
  bit 3: 0,0,0 -> 0,0,0
  bit 4: 1,0,0 -> 1,0,0
  bit 5: 1,1,1 -> 1,1,1
  bit 6: 0,0,0 -> 0,0,0
  bit 7: 1,1,1 -> 1,1,1
Deduce rule: and 0x0F.
Apply to 00011010:
  result = 00001010
Final: \boxed{00001010}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10011100 -> 01001110
  00101011 -> 10010101
  10111100 -> 01011110
Apply to: 01001010
### Reasoning:
<|cot_start|>Given examples:
  10011100 -> 01001110
  00101011 -> 10010101
  10111100 -> 01011110
Compare each bit position across the three examples:
  bit 0: 1,0,1 -> 0,1,0
  bit 1: 0,0,0 -> 1,0,1
  bit 2: 0,1,1 -> 0,0,0
  bit 3: 1,0,1 -> 0,1,1
  bit 4: 1,1,1 -> 1,0,1
  bit 5: 1,0,1 -> 1,1,1
  bit 6: 0,1,0 -> 1,0,1
  bit 7: 0,1,0 -> 0,1,0
Deduce rule: rotate right 1.
Apply to 01001010:
  result = 00100101
Final: \boxed{00100101}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  70,43 -> 7043
  71,34 -> 7134
  67,95 -> 6795
Apply to: 30,87
### Reasoning:
<|cot_start|>Examples:
  70,43 -> 7043
  71,34 -> 7134
  67,95 -> 6795
Check both candidate forms:
  concat(70,43)=7043  rev_concat(70,43)=4370  target=7043  concat
  concat(71,34)=7134  rev_concat(71,34)=3471  target=7134  concat
  concat(67,95)=6795  rev_concat(67,95)=9567  target=6795  concat
Conclude operator: concat.
Apply to (30, 87):  answer = 3087
Final: \boxed{3087}


### Task: numeral
### Problem:
Convert the Roman numeral XVI to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  X = 10  ->  0 + 10 = 10
  V = 5  ->  10 + 5 = 15
  I = 1  ->  15 + 1 = 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: gravity
### Problem:
A mass of 4 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 = 4 * 981.
Step-by-step multiplication:
  4 * 10^0 * 981 = 3924
  running total = 3924
So F = 3924 centiNewtons = 39.24 N.
Final: \boxed{39.24}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00100001 -> 01110100
  00111011 -> 01101110
  01100111 -> 00110010
Apply to: 00110011
### Reasoning:
<|cot_start|>Given examples:
  00100001 -> 01110100
  00111011 -> 01101110
  01100111 -> 00110010
Compare each bit position across the three examples:
  bit 0: 0,0,0 -> 0,0,0
  bit 1: 0,0,1 -> 1,1,0
  bit 2: 1,1,1 -> 1,1,1
  bit 3: 0,1,0 -> 1,0,1
  bit 4: 0,1,0 -> 0,1,0
  bit 5: 0,0,1 -> 1,1,0
  bit 6: 0,1,1 -> 0,1,1
  bit 7: 1,1,1 -> 0,0,0
Deduce rule: xor 0x55.
Apply to 00110011:
  result = 01100110
Final: \boxed{01100110}


### Task: unit
### Problem:
Convert 46 hours to minutes.
### Reasoning:
<|cot_start|>Conversion factor: 1 hours = 60 minutes.
So 46 hours = 46 * 60 minutes.
Compute step by step:
  4 * 10^1 * 60 = 2400
  running total = 2400
  6 * 10^0 * 60 = 360
  running total = 2760
Final: \boxed{2760}


### Task: unit
### Problem:
Convert 73 hours to minutes.
### Reasoning:
<|cot_start|>Conversion factor: 1 hours = 60 minutes.
So 73 hours = 73 * 60 minutes.
Compute step by step:
  7 * 10^1 * 60 = 4200
  running total = 4200
  3 * 10^0 * 60 = 180
  running total = 4380
Final: \boxed{4380}


### Task: gravity
### Problem:
A mass of 18 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 = 18 * 981.
Step-by-step multiplication:
  1 * 10^1 * 981 = 9810
  running total = 9810
  8 * 10^0 * 981 = 7848
  running total = 17658
So F = 17658 centiNewtons = 176.58 N.
Final: \boxed{176.58}


### 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 1 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 = 1 * 981.
Step-by-step multiplication:
  1 * 10^0 * 981 = 981
  running total = 981
So F = 981 centiNewtons = 9.81 N.
Final: \boxed{9.81}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  83,77 -> 160
  16,27 -> 43
  90,69 -> 159
Apply to: 82,27
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  83,77: '+' gives 160; target=160  MATCH
  83,77: '-' gives 6; target=160  no
  83,77: '*' gives 6391; target=160  no
  83,77: 'concat' gives 8377; target=160  no
  83,77: 'rev_concat' gives 7783; target=160  no
  83,77: 'max*min+sum' gives 6551; target=160  no
  83,77: 'digitsum2' gives 625; target=160  no
  16,27: '+' gives 43; target=43  MATCH
  16,27: '-' gives 11; target=43  no
  16,27: '*' gives 432; target=43  no
  16,27: 'concat' gives 1627; target=43  no
  16,27: 'rev_concat' gives 2716; target=43  no
  16,27: 'max*min+sum' gives 475; target=43  no
  16,27: 'digitsum2' gives 256; target=43  no
  90,69: '+' gives 159; target=159  MATCH
  90,69: '-' gives 21; target=159  no
  90,69: '*' gives 6210; target=159  no
  90,69: 'concat' gives 9069; target=159  no
  90,69: 'rev_concat' gives 6990; target=159  no
  90,69: 'max*min+sum' gives 6369; target=159  no
  90,69: 'digitsum2' gives 576; target=159  no
The only operator consistent with all examples is '+'.
Apply to (82, 27):
  result = 109
Final: \boxed{109}


### Task: numeral
### Problem:
Convert the Roman numeral LXXIX 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
  IX = 9  ->  70 + 9 = 79
Final: \boxed{79}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  94,68 -> 9468
  18,41 -> 1841
  39,25 -> 3925
Apply to: 29,65
### Reasoning:
<|cot_start|>Examples:
  94,68 -> 9468
  18,41 -> 1841
  39,25 -> 3925
Check both candidate forms:
  concat(94,68)=9468  rev_concat(94,68)=6894  target=9468  concat
  concat(18,41)=1841  rev_concat(18,41)=4118  target=1841  concat
  concat(39,25)=3925  rev_concat(39,25)=2539  target=3925  concat
Conclude operator: concat.
Apply to (29, 65):  answer = 2965
Final: \boxed{2965}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  43,35 -> 4335
  61,87 -> 6187
  67,71 -> 6771
Apply to: 49,52
### Reasoning:
<|cot_start|>Examples:
  43,35 -> 4335
  61,87 -> 6187
  67,71 -> 6771
Check both candidate forms:
  concat(43,35)=4335  rev_concat(43,35)=3543  target=4335  concat
  concat(61,87)=6187  rev_concat(61,87)=8761  target=6187  concat
  concat(67,71)=6771  rev_concat(67,71)=7167  target=6771  concat
Conclude operator: concat.
Apply to (49, 52):  answer = 4952
Final: \boxed{4952}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  81,23 -> 1967
  97,71 -> 7055
  76,88 -> 6852
Apply to: 99,73
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  81,23: '+' gives 104; target=1967  no
  81,23: '-' gives 58; target=1967  no
  81,23: '*' gives 1863; target=1967  no
  81,23: 'concat' gives 8123; target=1967  no
  81,23: 'rev_concat' gives 2381; target=1967  no
  81,23: 'max*min+sum' gives 1967; target=1967  MATCH
  81,23: 'digitsum2' gives 196; target=1967  no
  97,71: '+' gives 168; target=7055  no
  97,71: '-' gives 26; target=7055  no
  97,71: '*' gives 6887; target=7055  no
  97,71: 'concat' gives 9771; target=7055  no
  97,71: 'rev_concat' gives 7197; target=7055  no
  97,71: 'max*min+sum' gives 7055; target=7055  MATCH
  97,71: 'digitsum2' gives 576; target=7055  no
  76,88: '+' gives 164; target=6852  no
  76,88: '-' gives 12; target=6852  no
  76,88: '*' gives 6688; target=6852  no
  76,88: 'concat' gives 7688; target=6852  no
  76,88: 'rev_concat' gives 8876; target=6852  no
  76,88: 'max*min+sum' gives 6852; target=6852  MATCH
  76,88: 'digitsum2' gives 841; target=6852  no
The only operator consistent with all examples is 'max*min+sum'.
Apply to (99, 73):
  result = 7399
Final: \boxed{7399}


### Task: gravity
### Problem:
A mass of 6 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 = 6 * 981.
Step-by-step multiplication:
  6 * 10^0 * 981 = 5886
  running total = 5886
So F = 5886 centiNewtons = 58.86 N.
Final: \boxed{58.86}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  20,37 -> 144
  91,76 -> 529
  55,96 -> 625
Apply to: 68,94
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  20,37: '+' gives 57; target=144  no
  20,37: '-' gives 17; target=144  no
  20,37: '*' gives 740; target=144  no
  20,37: 'concat' gives 2037; target=144  no
  20,37: 'rev_concat' gives 3720; target=144  no
  20,37: 'max*min+sum' gives 797; target=144  no
  20,37: 'digitsum2' gives 144; target=144  MATCH
  91,76: '+' gives 167; target=529  no
  91,76: '-' gives 15; target=529  no
  91,76: '*' gives 6916; target=529  no
  91,76: 'concat' gives 9176; target=529  no
  91,76: 'rev_concat' gives 7691; target=529  no
  91,76: 'max*min+sum' gives 7083; target=529  no
  91,76: 'digitsum2' gives 529; target=529  MATCH
  55,96: '+' gives 151; target=625  no
  55,96: '-' gives 41; target=625  no
  55,96: '*' gives 5280; target=625  no
  55,96: 'concat' gives 5596; target=625  no
  55,96: 'rev_concat' gives 9655; target=625  no
  55,96: 'max*min+sum' gives 5431; target=625  no
  55,96: 'digitsum2' gives 625; target=625  MATCH
The only operator consistent with all examples is 'digitsum2'.
Apply to (68, 94):
  result = 729
Final: \boxed{729}


### Task: unit
### Problem:
Convert 43 litres to millilitres.
### Reasoning:
<|cot_start|>Conversion factor: 1 litres = 1000 millilitres.
So 43 litres = 43 * 1000 millilitres.
Compute step by step:
  4 * 10^1 * 1000 = 40000
  running total = 40000
  3 * 10^0 * 1000 = 3000
  running total = 43000
Final: \boxed{43000}


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


### Task: gravity
### Problem:
A mass of 8 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 = 8 * 981.
Step-by-step multiplication:
  8 * 10^0 * 981 = 7848
  running total = 7848
So F = 7848 centiNewtons = 78.48 N.
Final: \boxed{78.48}


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


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10100011 -> 00000011
  00000101 -> 00000101
  10000000 -> 00000000
Apply to: 11010111
### Reasoning:
<|cot_start|>Given examples:
  10100011 -> 00000011
  00000101 -> 00000101
  10000000 -> 00000000
Compare each bit position across the three examples:
  bit 0: 1,0,1 -> 0,0,0
  bit 1: 0,0,0 -> 0,0,0
  bit 2: 1,0,0 -> 0,0,0
  bit 3: 0,0,0 -> 0,0,0
  bit 4: 0,0,0 -> 0,0,0
  bit 5: 0,1,0 -> 0,1,0
  bit 6: 1,0,0 -> 1,0,0
  bit 7: 1,1,0 -> 1,1,0
Deduce rule: and 0x0F.
Apply to 11010111:
  result = 00000111
Final: \boxed{00000111}


### Task: numeral
### Problem:
Convert the Roman numeral LVII 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
Final: \boxed{57}


### Task: gravity
### Problem:
A mass of 29 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 = 29 * 981.
Step-by-step multiplication:
  2 * 10^1 * 981 = 19620
  running total = 19620
  9 * 10^0 * 981 = 8829
  running total = 28449
So F = 28449 centiNewtons = 284.49 N.
Final: \boxed{284.49}


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


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


### Task: unit
### Problem:
Convert 65 kilometres to metres.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilometres = 1000 metres.
So 65 kilometres = 65 * 1000 metres.
Compute step by step:
  6 * 10^1 * 1000 = 60000
  running total = 60000
  5 * 10^0 * 1000 = 5000
  running total = 65000
Final: \boxed{65000}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  41,30 -> 64
  93,93 -> 576
  23,24 -> 121
Apply to: 78,87
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  41,30: '+' gives 71; target=64  no
  41,30: '-' gives 11; target=64  no
  41,30: '*' gives 1230; target=64  no
  41,30: 'concat' gives 4130; target=64  no
  41,30: 'rev_concat' gives 3041; target=64  no
  41,30: 'max*min+sum' gives 1301; target=64  no
  41,30: 'digitsum2' gives 64; target=64  MATCH
  93,93: '+' gives 186; target=576  no
  93,93: '-' gives 0; target=576  no
  93,93: '*' gives 8649; target=576  no
  93,93: 'concat' gives 9393; target=576  no
  93,93: 'rev_concat' gives 9393; target=576  no
  93,93: 'max*min+sum' gives 8835; target=576  no
  93,93: 'digitsum2' gives 576; target=576  MATCH
  23,24: '+' gives 47; target=121  no
  23,24: '-' gives 1; target=121  no
  23,24: '*' gives 552; target=121  no
  23,24: 'concat' gives 2324; target=121  no
  23,24: 'rev_concat' gives 2423; target=121  no
  23,24: 'max*min+sum' gives 599; target=121  no
  23,24: 'digitsum2' gives 121; target=121  MATCH
The only operator consistent with all examples is 'digitsum2'.
Apply to (78, 87):
  result = 900
Final: \boxed{900}


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


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  40,20 -> 4020
  77,43 -> 7743
  23,16 -> 2316
Apply to: 58,21
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  40,20: '+' gives 60; target=4020  no
  40,20: '-' gives 20; target=4020  no
  40,20: '*' gives 800; target=4020  no
  40,20: 'concat' gives 4020; target=4020  MATCH
  40,20: 'rev_concat' gives 2040; target=4020  no
  40,20: 'max*min+sum' gives 860; target=4020  no
  40,20: 'digitsum2' gives 36; target=4020  no
  77,43: '+' gives 120; target=7743  no
  77,43: '-' gives 34; target=7743  no
  77,43: '*' gives 3311; target=7743  no
  77,43: 'concat' gives 7743; target=7743  MATCH
  77,43: 'rev_concat' gives 4377; target=7743  no
  77,43: 'max*min+sum' gives 3431; target=7743  no
  77,43: 'digitsum2' gives 441; target=7743  no
  23,16: '+' gives 39; target=2316  no
  23,16: '-' gives 7; target=2316  no
  23,16: '*' gives 368; target=2316  no
  23,16: 'concat' gives 2316; target=2316  MATCH
  23,16: 'rev_concat' gives 1623; target=2316  no
  23,16: 'max*min+sum' gives 407; target=2316  no
  23,16: 'digitsum2' gives 144; target=2316  no
The only operator consistent with all examples is 'concat'.
Apply to (58, 21):
  result = 5821
Final: \boxed{5821}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10101101 -> 01011011
  10000101 -> 00001011
  00110111 -> 01101110
Apply to: 00001111
### Reasoning:
<|cot_start|>Given examples:
  10101101 -> 01011011
  10000101 -> 00001011
  00110111 -> 01101110
Compare each bit position across the three examples:
  bit 0: 1,1,0 -> 0,0,0
  bit 1: 0,0,0 -> 1,0,1
  bit 2: 1,0,1 -> 0,0,1
  bit 3: 0,0,1 -> 1,0,0
  bit 4: 1,0,0 -> 1,1,1
  bit 5: 1,1,1 -> 0,0,1
  bit 6: 0,0,1 -> 1,1,1
  bit 7: 1,1,1 -> 1,1,0
Deduce rule: rotate left 1.
Apply to 00001111:
  result = 00011110
Final: \boxed{00011110}


### Task: gravity
### Problem:
A mass of 18 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 = 18 * 981.
Step-by-step multiplication:
  1 * 10^1 * 981 = 9810
  running total = 9810
  8 * 10^0 * 981 = 7848
  running total = 17658
So F = 17658 centiNewtons = 176.58 N.
Final: \boxed{176.58}


### Task: gravity
### Problem:
A mass of 30 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 = 30 * 981.
Step-by-step multiplication:
  3 * 10^1 * 981 = 29430
  running total = 29430
  0 * 10^0 * 981 = 0
  running total = 29430
So F = 29430 centiNewtons = 294.30 N.
Final: \boxed{294.30}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01101010 -> 01010110
  10000011 -> 11000001
  11000100 -> 00100011
Apply to: 01110101
### Reasoning:
<|cot_start|>Given examples:
  01101010 -> 01010110
  10000011 -> 11000001
  11000100 -> 00100011
Compare each bit position across the three examples:
  bit 0: 0,1,1 -> 0,1,0
  bit 1: 1,0,1 -> 1,1,0
  bit 2: 1,0,0 -> 0,0,1
  bit 3: 0,0,0 -> 1,0,0
  bit 4: 1,0,0 -> 0,0,0
  bit 5: 0,0,1 -> 1,0,0
  bit 6: 1,1,0 -> 1,0,1
  bit 7: 0,1,0 -> 0,1,1
Deduce rule: reverse bits.
Apply to 01110101:
  result = 10101110
Final: \boxed{10101110}


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


### Task: unit
### Problem:
Convert 5 metres to centimetres.
### Reasoning:
<|cot_start|>Conversion factor: 1 metres = 100 centimetres.
So 5 metres = 5 * 100 centimetres.
Compute step by step:
  5 * 10^0 * 100 = 500
  running total = 500
Final: \boxed{500}


### Task: unit
### Problem:
Convert 68 kilograms to grams.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilograms = 1000 grams.
So 68 kilograms = 68 * 1000 grams.
Compute step by step:
  6 * 10^1 * 1000 = 60000
  running total = 60000
  8 * 10^0 * 1000 = 8000
  running total = 68000
Final: \boxed{68000}


### Task: numeral
### Problem:
Convert the Roman numeral XLVI to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  XL = 40  ->  0 + 40 = 40
  V = 5  ->  40 + 5 = 45
  I = 1  ->  45 + 1 = 46
Final: \boxed{46}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  81,90 -> 9
  66,89 -> 23
  98,56 -> 42
Apply to: 15,92
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  81,90: '+' gives 171; target=9  no
  81,90: '-' gives 9; target=9  MATCH
  81,90: '*' gives 7290; target=9  no
  81,90: 'concat' gives 8190; target=9  no
  81,90: 'rev_concat' gives 9081; target=9  no
  81,90: 'max*min+sum' gives 7461; target=9  no
  81,90: 'digitsum2' gives 324; target=9  no
  66,89: '+' gives 155; target=23  no
  66,89: '-' gives 23; target=23  MATCH
  66,89: '*' gives 5874; target=23  no
  66,89: 'concat' gives 6689; target=23  no
  66,89: 'rev_concat' gives 8966; target=23  no
  66,89: 'max*min+sum' gives 6029; target=23  no
  66,89: 'digitsum2' gives 841; target=23  no
  98,56: '+' gives 154; target=42  no
  98,56: '-' gives 42; target=42  MATCH
  98,56: '*' gives 5488; target=42  no
  98,56: 'concat' gives 9856; target=42  no
  98,56: 'rev_concat' gives 5698; target=42  no
  98,56: 'max*min+sum' gives 5642; target=42  no
  98,56: 'digitsum2' gives 784; target=42  no
The only operator consistent with all examples is '-'.
Apply to (15, 92):
  result = 77
Final: \boxed{77}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10111101 -> 00001101
  10011011 -> 00001011
  11010110 -> 00000110
Apply to: 01010111
### Reasoning:
<|cot_start|>Given examples:
  10111101 -> 00001101
  10011011 -> 00001011
  11010110 -> 00000110
Compare each bit position across the three examples:
  bit 0: 1,1,1 -> 0,0,0
  bit 1: 0,0,1 -> 0,0,0
  bit 2: 1,0,0 -> 0,0,0
  bit 3: 1,1,1 -> 0,0,0
  bit 4: 1,1,0 -> 1,1,0
  bit 5: 1,0,1 -> 1,0,1
  bit 6: 0,1,1 -> 0,1,1
  bit 7: 1,1,0 -> 1,1,0
Deduce rule: and 0x0F.
Apply to 01010111:
  result = 00000111
Final: \boxed{00000111}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01101000 -> 11010000
  00100010 -> 01000100
  11111011 -> 11110111
Apply to: 01000011
### Reasoning:
<|cot_start|>Given examples:
  01101000 -> 11010000
  00100010 -> 01000100
  11111011 -> 11110111
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 1,0,1
  bit 1: 1,0,1 -> 1,1,1
  bit 2: 1,1,1 -> 0,0,1
  bit 3: 0,0,1 -> 1,0,1
  bit 4: 1,0,1 -> 0,0,0
  bit 5: 0,0,0 -> 0,1,1
  bit 6: 0,1,1 -> 0,0,1
  bit 7: 0,0,1 -> 0,0,1
Deduce rule: rotate left 1.
Apply to 01000011:
  result = 10000110
Final: \boxed{10000110}


### Task: numeral
### Problem:
Convert the Roman numeral LXVII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  X = 10  ->  50 + 10 = 60
  V = 5  ->  60 + 5 = 65
  I = 1  ->  65 + 1 = 66
  I = 1  ->  66 + 1 = 67
Final: \boxed{67}


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


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


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00010100 -> 00101000
  00010101 -> 10101000
  00101110 -> 01110100
Apply to: 10111100
### Reasoning:
<|cot_start|>Given examples:
  00010100 -> 00101000
  00010101 -> 10101000
  00101110 -> 01110100
Compare each bit position across the three examples:
  bit 0: 0,0,0 -> 0,1,0
  bit 1: 0,0,0 -> 0,0,1
  bit 2: 0,0,1 -> 1,1,1
  bit 3: 1,1,0 -> 0,0,1
  bit 4: 0,0,1 -> 1,1,0
  bit 5: 1,1,1 -> 0,0,1
  bit 6: 0,0,1 -> 0,0,0
  bit 7: 0,1,0 -> 0,0,0
Deduce rule: reverse bits.
Apply to 10111100:
  result = 00111101
Final: \boxed{00111101}


### Task: gravity
### Problem:
A mass of 26 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 = 26 * 981.
Step-by-step multiplication:
  2 * 10^1 * 981 = 19620
  running total = 19620
  6 * 10^0 * 981 = 5886
  running total = 25506
So F = 25506 centiNewtons = 255.06 N.
Final: \boxed{255.06}