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


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10010100 -> 00111110
  11001011 -> 01100001
  11100001 -> 01001011
Apply to: 10011111
### Reasoning:
<|cot_start|>Given examples:
  10010100 -> 00111110
  11001011 -> 01100001
  11100001 -> 01001011
Compare each bit position across the three examples:
  bit 0: 1,1,1 -> 0,0,0
  bit 1: 0,1,1 -> 0,1,1
  bit 2: 0,0,1 -> 1,1,0
  bit 3: 1,0,0 -> 1,0,0
  bit 4: 0,1,0 -> 1,0,1
  bit 5: 1,0,0 -> 1,0,0
  bit 6: 0,1,0 -> 1,0,1
  bit 7: 0,1,1 -> 0,1,1
Deduce rule: xor 0xAA.
Apply to 10011111:
  result = 00110101
Final: \boxed{00110101}


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


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  15,86 -> 1586
  38,82 -> 3882
  10,67 -> 1067
Apply to: 11,63
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  15,86: '+' gives 101; target=1586  no
  15,86: '-' gives 71; target=1586  no
  15,86: '*' gives 1290; target=1586  no
  15,86: 'concat' gives 1586; target=1586  MATCH
  15,86: 'rev_concat' gives 8615; target=1586  no
  15,86: 'max*min+sum' gives 1391; target=1586  no
  15,86: 'digitsum2' gives 400; target=1586  no
  38,82: '+' gives 120; target=3882  no
  38,82: '-' gives 44; target=3882  no
  38,82: '*' gives 3116; target=3882  no
  38,82: 'concat' gives 3882; target=3882  MATCH
  38,82: 'rev_concat' gives 8238; target=3882  no
  38,82: 'max*min+sum' gives 3236; target=3882  no
  38,82: 'digitsum2' gives 441; target=3882  no
  10,67: '+' gives 77; target=1067  no
  10,67: '-' gives 57; target=1067  no
  10,67: '*' gives 670; target=1067  no
  10,67: 'concat' gives 1067; target=1067  MATCH
  10,67: 'rev_concat' gives 6710; target=1067  no
  10,67: 'max*min+sum' gives 747; target=1067  no
  10,67: 'digitsum2' gives 196; target=1067  no
The only operator consistent with all examples is 'concat'.
Apply to (11, 63):
  result = 1163
Final: \boxed{1163}


### Task: numeral
### Problem:
Convert the Roman numeral XXXI 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
  I = 1  ->  30 + 1 = 31
Final: \boxed{31}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  63,13 -> 50
  48,32 -> 16
  83,30 -> 53
Apply to: 20,63
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  63,13: '+' gives 76; target=50  no
  63,13: '-' gives 50; target=50  MATCH
  63,13: '*' gives 819; target=50  no
  63,13: 'concat' gives 6313; target=50  no
  63,13: 'rev_concat' gives 1363; target=50  no
  63,13: 'max*min+sum' gives 895; target=50  no
  63,13: 'digitsum2' gives 169; target=50  no
  48,32: '+' gives 80; target=16  no
  48,32: '-' gives 16; target=16  MATCH
  48,32: '*' gives 1536; target=16  no
  48,32: 'concat' gives 4832; target=16  no
  48,32: 'rev_concat' gives 3248; target=16  no
  48,32: 'max*min+sum' gives 1616; target=16  no
  48,32: 'digitsum2' gives 289; target=16  no
  83,30: '+' gives 113; target=53  no
  83,30: '-' gives 53; target=53  MATCH
  83,30: '*' gives 2490; target=53  no
  83,30: 'concat' gives 8330; target=53  no
  83,30: 'rev_concat' gives 3083; target=53  no
  83,30: 'max*min+sum' gives 2603; target=53  no
  83,30: 'digitsum2' gives 196; target=53  no
The only operator consistent with all examples is '-'.
Apply to (20, 63):
  result = 43
Final: \boxed{43}


### Task: unit
### Problem:
Convert 29 kilometres to metres.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilometres = 1000 metres.
So 29 kilometres = 29 * 1000 metres.
Compute step by step:
  2 * 10^1 * 1000 = 20000
  running total = 20000
  9 * 10^0 * 1000 = 9000
  running total = 29000
Final: \boxed{29000}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00001011 -> 11110100
  11010100 -> 00101011
  00101011 -> 11010100
Apply to: 10001110
### Reasoning:
<|cot_start|>Given examples:
  00001011 -> 11110100
  11010100 -> 00101011
  00101011 -> 11010100
Compare each bit position across the three examples:
  bit 0: 0,1,0 -> 1,0,1
  bit 1: 0,1,0 -> 1,0,1
  bit 2: 0,0,1 -> 1,1,0
  bit 3: 0,1,0 -> 1,0,1
  bit 4: 1,0,1 -> 0,1,0
  bit 5: 0,1,0 -> 1,0,1
  bit 6: 1,0,1 -> 0,1,0
  bit 7: 1,0,1 -> 0,1,0
Deduce rule: invert (NOT).
Apply to 10001110:
  result = 01110001
Final: \boxed{01110001}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00111011 -> 01101110
  11110010 -> 10100111
  10010000 -> 11000101
Apply to: 10011100
### Reasoning:
<|cot_start|>Given examples:
  00111011 -> 01101110
  11110010 -> 10100111
  10010000 -> 11000101
Compare each bit position across the three examples:
  bit 0: 0,1,1 -> 0,1,1
  bit 1: 0,1,0 -> 1,0,1
  bit 2: 1,1,0 -> 1,1,0
  bit 3: 1,1,1 -> 0,0,0
  bit 4: 1,0,0 -> 1,0,0
  bit 5: 0,0,0 -> 1,1,1
  bit 6: 1,1,0 -> 1,1,0
  bit 7: 1,0,0 -> 0,1,1
Deduce rule: xor 0x55.
Apply to 10011100:
  result = 11001001
Final: \boxed{11001001}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  96,70 -> 9670
  88,27 -> 8827
  13,86 -> 1386
Apply to: 60,94
### Reasoning:
<|cot_start|>Examples:
  96,70 -> 9670
  88,27 -> 8827
  13,86 -> 1386
Check both candidate forms:
  concat(96,70)=9670  rev_concat(96,70)=7096  target=9670  concat
  concat(88,27)=8827  rev_concat(88,27)=2788  target=8827  concat
  concat(13,86)=1386  rev_concat(13,86)=8613  target=1386  concat
Conclude operator: concat.
Apply to (60, 94):  answer = 6094
Final: \boxed{6094}


### Task: gravity
### Problem:
A mass of 32 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 = 32 * 981.
Step-by-step multiplication:
  3 * 10^1 * 981 = 29430
  running total = 29430
  2 * 10^0 * 981 = 1962
  running total = 31392
So F = 31392 centiNewtons = 313.92 N.
Final: \boxed{313.92}


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


### Task: numeral
### Problem:
Convert the Roman numeral XIII 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
  I = 1  ->  12 + 1 = 13
Final: \boxed{13}


### Task: unit
### Problem:
Convert 35 litres to millilitres.
### Reasoning:
<|cot_start|>Conversion factor: 1 litres = 1000 millilitres.
So 35 litres = 35 * 1000 millilitres.
Compute step by step:
  3 * 10^1 * 1000 = 30000
  running total = 30000
  5 * 10^0 * 1000 = 5000
  running total = 35000
Final: \boxed{35000}


### 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: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  65,35 -> 6535
  48,87 -> 4887
  78,84 -> 7884
Apply to: 16,16
### Reasoning:
<|cot_start|>Examples:
  65,35 -> 6535
  48,87 -> 4887
  78,84 -> 7884
Check both candidate forms:
  concat(65,35)=6535  rev_concat(65,35)=3565  target=6535  concat
  concat(48,87)=4887  rev_concat(48,87)=8748  target=4887  concat
  concat(78,84)=7884  rev_concat(78,84)=8478  target=7884  concat
Conclude operator: concat.
Apply to (16, 16):  answer = 1616
Final: \boxed{1616}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  34,26 -> 944
  32,98 -> 3266
  44,45 -> 2069
Apply to: 96,51
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  34,26: '+' gives 60; target=944  no
  34,26: '-' gives 8; target=944  no
  34,26: '*' gives 884; target=944  no
  34,26: 'concat' gives 3426; target=944  no
  34,26: 'rev_concat' gives 2634; target=944  no
  34,26: 'max*min+sum' gives 944; target=944  MATCH
  34,26: 'digitsum2' gives 225; target=944  no
  32,98: '+' gives 130; target=3266  no
  32,98: '-' gives 66; target=3266  no
  32,98: '*' gives 3136; target=3266  no
  32,98: 'concat' gives 3298; target=3266  no
  32,98: 'rev_concat' gives 9832; target=3266  no
  32,98: 'max*min+sum' gives 3266; target=3266  MATCH
  32,98: 'digitsum2' gives 484; target=3266  no
  44,45: '+' gives 89; target=2069  no
  44,45: '-' gives 1; target=2069  no
  44,45: '*' gives 1980; target=2069  no
  44,45: 'concat' gives 4445; target=2069  no
  44,45: 'rev_concat' gives 4544; target=2069  no
  44,45: 'max*min+sum' gives 2069; target=2069  MATCH
  44,45: 'digitsum2' gives 289; target=2069  no
The only operator consistent with all examples is 'max*min+sum'.
Apply to (96, 51):
  result = 5043
Final: \boxed{5043}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  24,49 -> 1249
  94,49 -> 4749
  84,56 -> 4844
Apply to: 33,10
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  24,49: '+' gives 73; target=1249  no
  24,49: '-' gives 25; target=1249  no
  24,49: '*' gives 1176; target=1249  no
  24,49: 'concat' gives 2449; target=1249  no
  24,49: 'rev_concat' gives 4924; target=1249  no
  24,49: 'max*min+sum' gives 1249; target=1249  MATCH
  24,49: 'digitsum2' gives 361; target=1249  no
  94,49: '+' gives 143; target=4749  no
  94,49: '-' gives 45; target=4749  no
  94,49: '*' gives 4606; target=4749  no
  94,49: 'concat' gives 9449; target=4749  no
  94,49: 'rev_concat' gives 4994; target=4749  no
  94,49: 'max*min+sum' gives 4749; target=4749  MATCH
  94,49: 'digitsum2' gives 676; target=4749  no
  84,56: '+' gives 140; target=4844  no
  84,56: '-' gives 28; target=4844  no
  84,56: '*' gives 4704; target=4844  no
  84,56: 'concat' gives 8456; target=4844  no
  84,56: 'rev_concat' gives 5684; target=4844  no
  84,56: 'max*min+sum' gives 4844; target=4844  MATCH
  84,56: 'digitsum2' gives 529; target=4844  no
The only operator consistent with all examples is 'max*min+sum'.
Apply to (33, 10):
  result = 373
Final: \boxed{373}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01110100 -> 00111010
  01011011 -> 10101101
  10000001 -> 11000000
Apply to: 10111101
### Reasoning:
<|cot_start|>Given examples:
  01110100 -> 00111010
  01011011 -> 10101101
  10000001 -> 11000000
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 0,1,1
  bit 1: 1,1,0 -> 0,0,1
  bit 2: 1,0,0 -> 1,1,0
  bit 3: 1,1,0 -> 1,0,0
  bit 4: 0,1,0 -> 1,1,0
  bit 5: 1,0,0 -> 0,1,0
  bit 6: 0,1,0 -> 1,0,0
  bit 7: 0,1,1 -> 0,1,0
Deduce rule: rotate right 1.
Apply to 10111101:
  result = 11011110
Final: \boxed{11011110}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  72,63 -> 7263
  42,87 -> 4287
  34,80 -> 3480
Apply to: 14,80
### Reasoning:
<|cot_start|>Examples:
  72,63 -> 7263
  42,87 -> 4287
  34,80 -> 3480
Check both candidate forms:
  concat(72,63)=7263  rev_concat(72,63)=6372  target=7263  concat
  concat(42,87)=4287  rev_concat(42,87)=8742  target=4287  concat
  concat(34,80)=3480  rev_concat(34,80)=8034  target=3480  concat
Conclude operator: concat.
Apply to (14, 80):  answer = 1480
Final: \boxed{1480}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  10,89 -> 324
  52,93 -> 361
  49,79 -> 841
Apply to: 38,84
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  10,89: '+' gives 99; target=324  no
  10,89: '-' gives 79; target=324  no
  10,89: '*' gives 890; target=324  no
  10,89: 'concat' gives 1089; target=324  no
  10,89: 'rev_concat' gives 8910; target=324  no
  10,89: 'max*min+sum' gives 989; target=324  no
  10,89: 'digitsum2' gives 324; target=324  MATCH
  52,93: '+' gives 145; target=361  no
  52,93: '-' gives 41; target=361  no
  52,93: '*' gives 4836; target=361  no
  52,93: 'concat' gives 5293; target=361  no
  52,93: 'rev_concat' gives 9352; target=361  no
  52,93: 'max*min+sum' gives 4981; target=361  no
  52,93: 'digitsum2' gives 361; target=361  MATCH
  49,79: '+' gives 128; target=841  no
  49,79: '-' gives 30; target=841  no
  49,79: '*' gives 3871; target=841  no
  49,79: 'concat' gives 4979; target=841  no
  49,79: 'rev_concat' gives 7949; target=841  no
  49,79: 'max*min+sum' gives 3999; target=841  no
  49,79: 'digitsum2' gives 841; target=841  MATCH
The only operator consistent with all examples is 'digitsum2'.
Apply to (38, 84):
  result = 529
Final: \boxed{529}


### 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: 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:
  44,72 -> 3284
  57,47 -> 2783
  17,43 -> 791
Apply to: 99,23
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  44,72: '+' gives 116; target=3284  no
  44,72: '-' gives 28; target=3284  no
  44,72: '*' gives 3168; target=3284  no
  44,72: 'concat' gives 4472; target=3284  no
  44,72: 'rev_concat' gives 7244; target=3284  no
  44,72: 'max*min+sum' gives 3284; target=3284  MATCH
  44,72: 'digitsum2' gives 289; target=3284  no
  57,47: '+' gives 104; target=2783  no
  57,47: '-' gives 10; target=2783  no
  57,47: '*' gives 2679; target=2783  no
  57,47: 'concat' gives 5747; target=2783  no
  57,47: 'rev_concat' gives 4757; target=2783  no
  57,47: 'max*min+sum' gives 2783; target=2783  MATCH
  57,47: 'digitsum2' gives 529; target=2783  no
  17,43: '+' gives 60; target=791  no
  17,43: '-' gives 26; target=791  no
  17,43: '*' gives 731; target=791  no
  17,43: 'concat' gives 1743; target=791  no
  17,43: 'rev_concat' gives 4317; target=791  no
  17,43: 'max*min+sum' gives 791; target=791  MATCH
  17,43: 'digitsum2' gives 225; target=791  no
The only operator consistent with all examples is 'max*min+sum'.
Apply to (99, 23):
  result = 2399
Final: \boxed{2399}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11011001 -> 11101100
  11101111 -> 11110111
  01100011 -> 10110001
Apply to: 01010010
### Reasoning:
<|cot_start|>Given examples:
  11011001 -> 11101100
  11101111 -> 11110111
  01100011 -> 10110001
Compare each bit position across the three examples:
  bit 0: 1,1,0 -> 1,1,1
  bit 1: 1,1,1 -> 1,1,0
  bit 2: 0,1,1 -> 1,1,1
  bit 3: 1,0,0 -> 0,1,1
  bit 4: 1,1,0 -> 1,0,0
  bit 5: 0,1,0 -> 1,1,0
  bit 6: 0,1,1 -> 0,1,0
  bit 7: 1,1,1 -> 0,1,1
Deduce rule: rotate right 1.
Apply to 01010010:
  result = 00101001
Final: \boxed{00101001}


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


### Task: unit
### Problem:
Convert 31 minutes to seconds.
### Reasoning:
<|cot_start|>Conversion factor: 1 minutes = 60 seconds.
So 31 minutes = 31 * 60 seconds.
Compute step by step:
  3 * 10^1 * 60 = 1800
  running total = 1800
  1 * 10^0 * 60 = 60
  running total = 1860
Final: \boxed{1860}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  15,21 -> 351
  26,60 -> 1646
  59,86 -> 5219
Apply to: 32,38
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  15,21: '+' gives 36; target=351  no
  15,21: '-' gives 6; target=351  no
  15,21: '*' gives 315; target=351  no
  15,21: 'concat' gives 1521; target=351  no
  15,21: 'rev_concat' gives 2115; target=351  no
  15,21: 'max*min+sum' gives 351; target=351  MATCH
  15,21: 'digitsum2' gives 81; target=351  no
  26,60: '+' gives 86; target=1646  no
  26,60: '-' gives 34; target=1646  no
  26,60: '*' gives 1560; target=1646  no
  26,60: 'concat' gives 2660; target=1646  no
  26,60: 'rev_concat' gives 6026; target=1646  no
  26,60: 'max*min+sum' gives 1646; target=1646  MATCH
  26,60: 'digitsum2' gives 196; target=1646  no
  59,86: '+' gives 145; target=5219  no
  59,86: '-' gives 27; target=5219  no
  59,86: '*' gives 5074; target=5219  no
  59,86: 'concat' gives 5986; target=5219  no
  59,86: 'rev_concat' gives 8659; target=5219  no
  59,86: 'max*min+sum' gives 5219; target=5219  MATCH
  59,86: 'digitsum2' gives 784; target=5219  no
The only operator consistent with all examples is 'max*min+sum'.
Apply to (32, 38):
  result = 1286
Final: \boxed{1286}


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


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


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  46,70 -> 7046
  15,79 -> 7915
  74,48 -> 4874
Apply to: 50,44
### Reasoning:
<|cot_start|>Examples:
  46,70 -> 7046
  15,79 -> 7915
  74,48 -> 4874
Check both candidate forms:
  concat(46,70)=4670  rev_concat(46,70)=7046  target=7046  rev_concat
  concat(15,79)=1579  rev_concat(15,79)=7915  target=7915  rev_concat
  concat(74,48)=7448  rev_concat(74,48)=4874  target=4874  rev_concat
Conclude operator: rev_concat.
Apply to (50, 44):  answer = 4450
Final: \boxed{4450}


### Task: numeral
### Problem:
Convert the Roman numeral XXVII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  X = 10  ->  0 + 10 = 10
  X = 10  ->  10 + 10 = 20
  V = 5  ->  20 + 5 = 25
  I = 1  ->  25 + 1 = 26
  I = 1  ->  26 + 1 = 27
Final: \boxed{27}


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


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  95,59 -> 9559
  29,99 -> 2999
  73,83 -> 7383
Apply to: 27,16
### Reasoning:
<|cot_start|>Examples:
  95,59 -> 9559
  29,99 -> 2999
  73,83 -> 7383
Check both candidate forms:
  concat(95,59)=9559  rev_concat(95,59)=5995  target=9559  concat
  concat(29,99)=2999  rev_concat(29,99)=9929  target=2999  concat
  concat(73,83)=7383  rev_concat(73,83)=8373  target=7383  concat
Conclude operator: concat.
Apply to (27, 16):  answer = 2716
Final: \boxed{2716}


### Task: numeral
### Problem:
Convert the Roman numeral LXXVIII 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
  I = 1  ->  77 + 1 = 78
Final: \boxed{78}


### 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: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01110110 -> 01100111
  11001001 -> 10011100
  00010001 -> 00010001
Apply to: 11010111
### Reasoning:
<|cot_start|>Given examples:
  01110110 -> 01100111
  11001001 -> 10011100
  00010001 -> 00010001
Compare each bit position across the three examples:
  bit 0: 0,1,0 -> 0,1,0
  bit 1: 1,1,0 -> 1,0,0
  bit 2: 1,0,0 -> 1,0,0
  bit 3: 1,0,1 -> 0,1,1
  bit 4: 0,1,0 -> 0,1,0
  bit 5: 1,0,0 -> 1,1,0
  bit 6: 1,0,0 -> 1,0,0
  bit 7: 0,1,1 -> 1,0,1
Deduce rule: swap nibbles.
Apply to 11010111:
  result = 01111101
Final: \boxed{01111101}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10110110 -> 01001001
  01101011 -> 10010100
  10011101 -> 01100010
Apply to: 11011100
### Reasoning:
<|cot_start|>Given examples:
  10110110 -> 01001001
  01101011 -> 10010100
  10011101 -> 01100010
Compare each bit position across the three examples:
  bit 0: 1,0,1 -> 0,1,0
  bit 1: 0,1,0 -> 1,0,1
  bit 2: 1,1,0 -> 0,0,1
  bit 3: 1,0,1 -> 0,1,0
  bit 4: 0,1,1 -> 1,0,0
  bit 5: 1,0,1 -> 0,1,0
  bit 6: 1,1,0 -> 0,0,1
  bit 7: 0,1,1 -> 1,0,0
Deduce rule: invert (NOT).
Apply to 11011100:
  result = 00100011
Final: \boxed{00100011}


### Task: gravity
### Problem:
A mass of 41 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 = 41 * 981.
Step-by-step multiplication:
  4 * 10^1 * 981 = 39240
  running total = 39240
  1 * 10^0 * 981 = 981
  running total = 40221
So F = 40221 centiNewtons = 402.21 N.
Final: \boxed{402.21}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  62,55 -> 5562
  19,52 -> 5219
  45,54 -> 5445
Apply to: 22,48
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  62,55: '+' gives 117; target=5562  no
  62,55: '-' gives 7; target=5562  no
  62,55: '*' gives 3410; target=5562  no
  62,55: 'concat' gives 6255; target=5562  no
  62,55: 'rev_concat' gives 5562; target=5562  MATCH
  62,55: 'max*min+sum' gives 3527; target=5562  no
  62,55: 'digitsum2' gives 324; target=5562  no
  19,52: '+' gives 71; target=5219  no
  19,52: '-' gives 33; target=5219  no
  19,52: '*' gives 988; target=5219  no
  19,52: 'concat' gives 1952; target=5219  no
  19,52: 'rev_concat' gives 5219; target=5219  MATCH
  19,52: 'max*min+sum' gives 1059; target=5219  no
  19,52: 'digitsum2' gives 289; target=5219  no
  45,54: '+' gives 99; target=5445  no
  45,54: '-' gives 9; target=5445  no
  45,54: '*' gives 2430; target=5445  no
  45,54: 'concat' gives 4554; target=5445  no
  45,54: 'rev_concat' gives 5445; target=5445  MATCH
  45,54: 'max*min+sum' gives 2529; target=5445  no
  45,54: 'digitsum2' gives 324; target=5445  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (22, 48):
  result = 4822
Final: \boxed{4822}


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


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  88,80 -> 8
  50,94 -> 44
  73,53 -> 20
Apply to: 85,91
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  88,80: '+' gives 168; target=8  no
  88,80: '-' gives 8; target=8  MATCH
  88,80: '*' gives 7040; target=8  no
  88,80: 'concat' gives 8880; target=8  no
  88,80: 'rev_concat' gives 8088; target=8  no
  88,80: 'max*min+sum' gives 7208; target=8  no
  88,80: 'digitsum2' gives 576; target=8  no
  50,94: '+' gives 144; target=44  no
  50,94: '-' gives 44; target=44  MATCH
  50,94: '*' gives 4700; target=44  no
  50,94: 'concat' gives 5094; target=44  no
  50,94: 'rev_concat' gives 9450; target=44  no
  50,94: 'max*min+sum' gives 4844; target=44  no
  50,94: 'digitsum2' gives 324; target=44  no
  73,53: '+' gives 126; target=20  no
  73,53: '-' gives 20; target=20  MATCH
  73,53: '*' gives 3869; target=20  no
  73,53: 'concat' gives 7353; target=20  no
  73,53: 'rev_concat' gives 5373; target=20  no
  73,53: 'max*min+sum' gives 3995; target=20  no
  73,53: 'digitsum2' gives 324; target=20  no
The only operator consistent with all examples is '-'.
Apply to (85, 91):
  result = 6
Final: \boxed{6}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01000001 -> 10000010
  00111111 -> 11111100
  01111111 -> 11111110
Apply to: 10110111
### Reasoning:
<|cot_start|>Given examples:
  01000001 -> 10000010
  00111111 -> 11111100
  01111111 -> 11111110
Compare each bit position across the three examples:
  bit 0: 0,0,0 -> 1,1,1
  bit 1: 1,0,1 -> 0,1,1
  bit 2: 0,1,1 -> 0,1,1
  bit 3: 0,1,1 -> 0,1,1
  bit 4: 0,1,1 -> 0,1,1
  bit 5: 0,1,1 -> 0,1,1
  bit 6: 0,1,1 -> 1,0,1
  bit 7: 1,1,1 -> 0,0,0
Deduce rule: reverse bits.
Apply to 10110111:
  result = 11101101
Final: \boxed{11101101}


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


### Task: numeral
### Problem:
Convert the Roman numeral XXIV to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  X = 10  ->  0 + 10 = 10
  X = 10  ->  10 + 10 = 20
  IV = 4  ->  20 + 4 = 24
Final: \boxed{24}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  17,58 -> 986
  24,82 -> 1968
  73,30 -> 2190
Apply to: 58,38
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  17,58: '+' gives 75; target=986  no
  17,58: '-' gives 41; target=986  no
  17,58: '*' gives 986; target=986  MATCH
  17,58: 'concat' gives 1758; target=986  no
  17,58: 'rev_concat' gives 5817; target=986  no
  17,58: 'max*min+sum' gives 1061; target=986  no
  17,58: 'digitsum2' gives 441; target=986  no
  24,82: '+' gives 106; target=1968  no
  24,82: '-' gives 58; target=1968  no
  24,82: '*' gives 1968; target=1968  MATCH
  24,82: 'concat' gives 2482; target=1968  no
  24,82: 'rev_concat' gives 8224; target=1968  no
  24,82: 'max*min+sum' gives 2074; target=1968  no
  24,82: 'digitsum2' gives 256; target=1968  no
  73,30: '+' gives 103; target=2190  no
  73,30: '-' gives 43; target=2190  no
  73,30: '*' gives 2190; target=2190  MATCH
  73,30: 'concat' gives 7330; target=2190  no
  73,30: 'rev_concat' gives 3073; target=2190  no
  73,30: 'max*min+sum' gives 2293; target=2190  no
  73,30: 'digitsum2' gives 169; target=2190  no
The only operator consistent with all examples is '*'.
Apply to (58, 38):
  result = 2204
Final: \boxed{2204}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  79,72 -> 7972
  24,40 -> 2440
  87,54 -> 8754
Apply to: 97,82
### Reasoning:
<|cot_start|>Examples:
  79,72 -> 7972
  24,40 -> 2440
  87,54 -> 8754
Check both candidate forms:
  concat(79,72)=7972  rev_concat(79,72)=7279  target=7972  concat
  concat(24,40)=2440  rev_concat(24,40)=4024  target=2440  concat
  concat(87,54)=8754  rev_concat(87,54)=5487  target=8754  concat
Conclude operator: concat.
Apply to (97, 82):  answer = 9782
Final: \boxed{9782}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10001000 -> 01110111
  00110110 -> 11001001
  11000101 -> 00111010
Apply to: 10000011
### Reasoning:
<|cot_start|>Given examples:
  10001000 -> 01110111
  00110110 -> 11001001
  11000101 -> 00111010
Compare each bit position across the three examples:
  bit 0: 1,0,1 -> 0,1,0
  bit 1: 0,0,1 -> 1,1,0
  bit 2: 0,1,0 -> 1,0,1
  bit 3: 0,1,0 -> 1,0,1
  bit 4: 1,0,0 -> 0,1,1
  bit 5: 0,1,1 -> 1,0,0
  bit 6: 0,1,0 -> 1,0,1
  bit 7: 0,0,1 -> 1,1,0
Deduce rule: invert (NOT).
Apply to 10000011:
  result = 01111100
Final: \boxed{01111100}


### Task: gravity
### Problem:
A mass of 36 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 = 36 * 981.
Step-by-step multiplication:
  3 * 10^1 * 981 = 29430
  running total = 29430
  6 * 10^0 * 981 = 5886
  running total = 35316
So F = 35316 centiNewtons = 353.16 N.
Final: \boxed{353.16}


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


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11001111 -> 10011010
  10001110 -> 11011011
  01101010 -> 00111111
Apply to: 00101000
### Reasoning:
<|cot_start|>Given examples:
  11001111 -> 10011010
  10001110 -> 11011011
  01101010 -> 00111111
Compare each bit position across the three examples:
  bit 0: 1,1,0 -> 1,1,0
  bit 1: 1,0,1 -> 0,1,0
  bit 2: 0,0,1 -> 0,0,1
  bit 3: 0,0,0 -> 1,1,1
  bit 4: 1,1,1 -> 1,1,1
  bit 5: 1,1,0 -> 0,0,1
  bit 6: 1,1,1 -> 1,1,1
  bit 7: 1,0,0 -> 0,1,1
Deduce rule: xor 0x55.
Apply to 00101000:
  result = 01111101
Final: \boxed{01111101}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01110100 -> 00000100
  11000101 -> 00000101
  00000111 -> 00000111
Apply to: 01100000
### Reasoning:
<|cot_start|>Given examples:
  01110100 -> 00000100
  11000101 -> 00000101
  00000111 -> 00000111
Compare each bit position across the three examples:
  bit 0: 0,1,0 -> 0,0,0
  bit 1: 1,1,0 -> 0,0,0
  bit 2: 1,0,0 -> 0,0,0
  bit 3: 1,0,0 -> 0,0,0
  bit 4: 0,0,0 -> 0,0,0
  bit 5: 1,1,1 -> 1,1,1
  bit 6: 0,0,1 -> 0,0,1
  bit 7: 0,1,1 -> 0,1,1
Deduce rule: and 0x0F.
Apply to 01100000:
  result = 00000000
Final: \boxed{00000000}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00000000 -> 11111111
  01001001 -> 10110110
  10000011 -> 01111100
Apply to: 01101011
### Reasoning:
<|cot_start|>Given examples:
  00000000 -> 11111111
  01001001 -> 10110110
  10000011 -> 01111100
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 1,1,0
  bit 1: 0,1,0 -> 1,0,1
  bit 2: 0,0,0 -> 1,1,1
  bit 3: 0,0,0 -> 1,1,1
  bit 4: 0,1,0 -> 1,0,1
  bit 5: 0,0,0 -> 1,1,1
  bit 6: 0,0,1 -> 1,1,0
  bit 7: 0,1,1 -> 1,0,0
Deduce rule: invert (NOT).
Apply to 01101011:
  result = 10010100
Final: \boxed{10010100}


### Task: gravity
### Problem:
A mass of 14 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 = 14 * 981.
Step-by-step multiplication:
  1 * 10^1 * 981 = 9810
  running total = 9810
  4 * 10^0 * 981 = 3924
  running total = 13734
So F = 13734 centiNewtons = 137.34 N.
Final: \boxed{137.34}


### Task: gravity
### Problem:
A mass of 45 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 = 45 * 981.
Step-by-step multiplication:
  4 * 10^1 * 981 = 39240
  running total = 39240
  5 * 10^0 * 981 = 4905
  running total = 44145
So F = 44145 centiNewtons = 441.45 N.
Final: \boxed{441.45}


### Task: unit
### Problem:
Convert 54 days to hours.
### Reasoning:
<|cot_start|>Conversion factor: 1 days = 24 hours.
So 54 days = 54 * 24 hours.
Compute step by step:
  5 * 10^1 * 24 = 1200
  running total = 1200
  4 * 10^0 * 24 = 96
  running total = 1296
Final: \boxed{1296}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  57,26 -> 5726
  18,92 -> 1892
  66,78 -> 6678
Apply to: 24,22
### Reasoning:
<|cot_start|>Examples:
  57,26 -> 5726
  18,92 -> 1892
  66,78 -> 6678
Check both candidate forms:
  concat(57,26)=5726  rev_concat(57,26)=2657  target=5726  concat
  concat(18,92)=1892  rev_concat(18,92)=9218  target=1892  concat
  concat(66,78)=6678  rev_concat(66,78)=7866  target=6678  concat
Conclude operator: concat.
Apply to (24, 22):  answer = 2422
Final: \boxed{2422}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  98,46 -> 9846
  59,26 -> 5926
  14,34 -> 1434
Apply to: 89,48
### Reasoning:
<|cot_start|>Examples:
  98,46 -> 9846
  59,26 -> 5926
  14,34 -> 1434
Check both candidate forms:
  concat(98,46)=9846  rev_concat(98,46)=4698  target=9846  concat
  concat(59,26)=5926  rev_concat(59,26)=2659  target=5926  concat
  concat(14,34)=1434  rev_concat(14,34)=3414  target=1434  concat
Conclude operator: concat.
Apply to (89, 48):  answer = 8948
Final: \boxed{8948}


### Task: unit
### Problem:
Convert 95 kilograms to grams.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilograms = 1000 grams.
So 95 kilograms = 95 * 1000 grams.
Compute step by step:
  9 * 10^1 * 1000 = 90000
  running total = 90000
  5 * 10^0 * 1000 = 5000
  running total = 95000
Final: \boxed{95000}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01100101 -> 00000101
  01111100 -> 00001100
  10111111 -> 00001111
Apply to: 11101100
### Reasoning:
<|cot_start|>Given examples:
  01100101 -> 00000101
  01111100 -> 00001100
  10111111 -> 00001111
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 0,0,0
  bit 1: 1,1,0 -> 0,0,0
  bit 2: 1,1,1 -> 0,0,0
  bit 3: 0,1,1 -> 0,0,0
  bit 4: 0,1,1 -> 0,1,1
  bit 5: 1,1,1 -> 1,1,1
  bit 6: 0,0,1 -> 0,0,1
  bit 7: 1,0,1 -> 1,0,1
Deduce rule: and 0x0F.
Apply to 11101100:
  result = 00001100
Final: \boxed{00001100}


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


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


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  62,81 -> 6281
  14,54 -> 1454
  64,45 -> 6445
Apply to: 46,28
### Reasoning:
<|cot_start|>Examples:
  62,81 -> 6281
  14,54 -> 1454
  64,45 -> 6445
Check both candidate forms:
  concat(62,81)=6281  rev_concat(62,81)=8162  target=6281  concat
  concat(14,54)=1454  rev_concat(14,54)=5414  target=1454  concat
  concat(64,45)=6445  rev_concat(64,45)=4564  target=6445  concat
Conclude operator: concat.
Apply to (46, 28):  answer = 4628
Final: \boxed{4628}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10101001 -> 10010101
  01000100 -> 00100010
  00010000 -> 00001000
Apply to: 11111011
### Reasoning:
<|cot_start|>Given examples:
  10101001 -> 10010101
  01000100 -> 00100010
  00010000 -> 00001000
Compare each bit position across the three examples:
  bit 0: 1,0,0 -> 1,0,0
  bit 1: 0,1,0 -> 0,0,0
  bit 2: 1,0,0 -> 0,1,0
  bit 3: 0,0,1 -> 1,0,0
  bit 4: 1,0,0 -> 0,0,1
  bit 5: 0,1,0 -> 1,0,0
  bit 6: 0,0,0 -> 0,1,0
  bit 7: 1,0,0 -> 1,0,0
Deduce rule: reverse bits.
Apply to 11111011:
  result = 11011111
Final: \boxed{11011111}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00010110 -> 11101001
  01001111 -> 10110000
  01010110 -> 10101001
Apply to: 11110000
### Reasoning:
<|cot_start|>Given examples:
  00010110 -> 11101001
  01001111 -> 10110000
  01010110 -> 10101001
Compare each bit position across the three examples:
  bit 0: 0,0,0 -> 1,1,1
  bit 1: 0,1,1 -> 1,0,0
  bit 2: 0,0,0 -> 1,1,1
  bit 3: 1,0,1 -> 0,1,0
  bit 4: 0,1,0 -> 1,0,1
  bit 5: 1,1,1 -> 0,0,0
  bit 6: 1,1,1 -> 0,0,0
  bit 7: 0,1,0 -> 1,0,1
Deduce rule: invert (NOT).
Apply to 11110000:
  result = 00001111
Final: \boxed{00001111}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00000000 -> 10101010
  00101111 -> 10000101
  10101101 -> 00000111
Apply to: 10101100
### Reasoning:
<|cot_start|>Given examples:
  00000000 -> 10101010
  00101111 -> 10000101
  10101101 -> 00000111
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 1,1,0
  bit 1: 0,0,0 -> 0,0,0
  bit 2: 0,1,1 -> 1,0,0
  bit 3: 0,0,0 -> 0,0,0
  bit 4: 0,1,1 -> 1,0,0
  bit 5: 0,1,1 -> 0,1,1
  bit 6: 0,1,0 -> 1,0,1
  bit 7: 0,1,1 -> 0,1,1
Deduce rule: xor 0xAA.
Apply to 10101100:
  result = 00000110
Final: \boxed{00000110}


### Task: gravity
### Problem:
A mass of 11 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 = 11 * 981.
Step-by-step multiplication:
  1 * 10^1 * 981 = 9810
  running total = 9810
  1 * 10^0 * 981 = 981
  running total = 10791
So F = 10791 centiNewtons = 107.91 N.
Final: \boxed{107.91}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11001000 -> 01100100
  00010000 -> 00001000
  10001000 -> 01000100
Apply to: 10101001
### Reasoning:
<|cot_start|>Given examples:
  11001000 -> 01100100
  00010000 -> 00001000
  10001000 -> 01000100
Compare each bit position across the three examples:
  bit 0: 1,0,1 -> 0,0,0
  bit 1: 1,0,0 -> 1,0,1
  bit 2: 0,0,0 -> 1,0,0
  bit 3: 0,1,0 -> 0,0,0
  bit 4: 1,0,1 -> 0,1,0
  bit 5: 0,0,0 -> 1,0,1
  bit 6: 0,0,0 -> 0,0,0
  bit 7: 0,0,0 -> 0,0,0
Deduce rule: rotate right 1.
Apply to 10101001:
  result = 11010100
Final: \boxed{11010100}


### Task: unit
### Problem:
Convert 45 kilograms to grams.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilograms = 1000 grams.
So 45 kilograms = 45 * 1000 grams.
Compute step by step:
  4 * 10^1 * 1000 = 40000
  running total = 40000
  5 * 10^0 * 1000 = 5000
  running total = 45000
Final: \boxed{45000}


### Task: unit
### Problem:
Convert 24 hours to minutes.
### Reasoning:
<|cot_start|>Conversion factor: 1 hours = 60 minutes.
So 24 hours = 24 * 60 minutes.
Compute step by step:
  2 * 10^1 * 60 = 1200
  running total = 1200
  4 * 10^0 * 60 = 240
  running total = 1440
Final: \boxed{1440}


### Task: numeral
### Problem:
Convert the Roman numeral LXXI 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
  I = 1  ->  70 + 1 = 71
Final: \boxed{71}


### Task: unit
### Problem:
Convert 64 hours to minutes.
### Reasoning:
<|cot_start|>Conversion factor: 1 hours = 60 minutes.
So 64 hours = 64 * 60 minutes.
Compute step by step:
  6 * 10^1 * 60 = 3600
  running total = 3600
  4 * 10^0 * 60 = 240
  running total = 3840
Final: \boxed{3840}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  23,81 -> 2381
  81,17 -> 8117
  13,53 -> 1353
Apply to: 64,87
### Reasoning:
<|cot_start|>Examples:
  23,81 -> 2381
  81,17 -> 8117
  13,53 -> 1353
Check both candidate forms:
  concat(23,81)=2381  rev_concat(23,81)=8123  target=2381  concat
  concat(81,17)=8117  rev_concat(81,17)=1781  target=8117  concat
  concat(13,53)=1353  rev_concat(13,53)=5313  target=1353  concat
Conclude operator: concat.
Apply to (64, 87):  answer = 6487
Final: \boxed{6487}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  44,47 -> 2159
  12,89 -> 1169
  97,89 -> 8819
Apply to: 33,44
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  44,47: '+' gives 91; target=2159  no
  44,47: '-' gives 3; target=2159  no
  44,47: '*' gives 2068; target=2159  no
  44,47: 'concat' gives 4447; target=2159  no
  44,47: 'rev_concat' gives 4744; target=2159  no
  44,47: 'max*min+sum' gives 2159; target=2159  MATCH
  44,47: 'digitsum2' gives 361; target=2159  no
  12,89: '+' gives 101; target=1169  no
  12,89: '-' gives 77; target=1169  no
  12,89: '*' gives 1068; target=1169  no
  12,89: 'concat' gives 1289; target=1169  no
  12,89: 'rev_concat' gives 8912; target=1169  no
  12,89: 'max*min+sum' gives 1169; target=1169  MATCH
  12,89: 'digitsum2' gives 400; target=1169  no
  97,89: '+' gives 186; target=8819  no
  97,89: '-' gives 8; target=8819  no
  97,89: '*' gives 8633; target=8819  no
  97,89: 'concat' gives 9789; target=8819  no
  97,89: 'rev_concat' gives 8997; target=8819  no
  97,89: 'max*min+sum' gives 8819; target=8819  MATCH
  97,89: 'digitsum2' gives 1089; target=8819  no
The only operator consistent with all examples is 'max*min+sum'.
Apply to (33, 44):
  result = 1529
Final: \boxed{1529}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00001011 -> 11010000
  11110100 -> 00101111
  10101111 -> 11110101
Apply to: 00000001
### Reasoning:
<|cot_start|>Given examples:
  00001011 -> 11010000
  11110100 -> 00101111
  10101111 -> 11110101
Compare each bit position across the three examples:
  bit 0: 0,1,1 -> 1,0,1
  bit 1: 0,1,0 -> 1,0,1
  bit 2: 0,1,1 -> 0,1,1
  bit 3: 0,1,0 -> 1,0,1
  bit 4: 1,0,1 -> 0,1,0
  bit 5: 0,1,1 -> 0,1,1
  bit 6: 1,0,1 -> 0,1,0
  bit 7: 1,0,1 -> 0,1,1
Deduce rule: reverse bits.
Apply to 00000001:
  result = 10000000
Final: \boxed{10000000}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  59,44 -> 103
  69,46 -> 115
  13,61 -> 74
Apply to: 13,68
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  59,44: '+' gives 103; target=103  MATCH
  59,44: '-' gives 15; target=103  no
  59,44: '*' gives 2596; target=103  no
  59,44: 'concat' gives 5944; target=103  no
  59,44: 'rev_concat' gives 4459; target=103  no
  59,44: 'max*min+sum' gives 2699; target=103  no
  59,44: 'digitsum2' gives 484; target=103  no
  69,46: '+' gives 115; target=115  MATCH
  69,46: '-' gives 23; target=115  no
  69,46: '*' gives 3174; target=115  no
  69,46: 'concat' gives 6946; target=115  no
  69,46: 'rev_concat' gives 4669; target=115  no
  69,46: 'max*min+sum' gives 3289; target=115  no
  69,46: 'digitsum2' gives 625; target=115  no
  13,61: '+' gives 74; target=74  MATCH
  13,61: '-' gives 48; target=74  no
  13,61: '*' gives 793; target=74  no
  13,61: 'concat' gives 1361; target=74  no
  13,61: 'rev_concat' gives 6113; target=74  no
  13,61: 'max*min+sum' gives 867; target=74  no
  13,61: 'digitsum2' gives 121; target=74  no
The only operator consistent with all examples is '+'.
Apply to (13, 68):
  result = 81
Final: \boxed{81}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  56,22 -> 1232
  22,58 -> 1276
  72,26 -> 1872
Apply to: 52,83
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  56,22: '+' gives 78; target=1232  no
  56,22: '-' gives 34; target=1232  no
  56,22: '*' gives 1232; target=1232  MATCH
  56,22: 'concat' gives 5622; target=1232  no
  56,22: 'rev_concat' gives 2256; target=1232  no
  56,22: 'max*min+sum' gives 1310; target=1232  no
  56,22: 'digitsum2' gives 225; target=1232  no
  22,58: '+' gives 80; target=1276  no
  22,58: '-' gives 36; target=1276  no
  22,58: '*' gives 1276; target=1276  MATCH
  22,58: 'concat' gives 2258; target=1276  no
  22,58: 'rev_concat' gives 5822; target=1276  no
  22,58: 'max*min+sum' gives 1356; target=1276  no
  22,58: 'digitsum2' gives 289; target=1276  no
  72,26: '+' gives 98; target=1872  no
  72,26: '-' gives 46; target=1872  no
  72,26: '*' gives 1872; target=1872  MATCH
  72,26: 'concat' gives 7226; target=1872  no
  72,26: 'rev_concat' gives 2672; target=1872  no
  72,26: 'max*min+sum' gives 1970; target=1872  no
  72,26: 'digitsum2' gives 289; target=1872  no
The only operator consistent with all examples is '*'.
Apply to (52, 83):
  result = 4316
Final: \boxed{4316}


### Task: numeral
### Problem:
Convert the Roman numeral XXIV to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  X = 10  ->  0 + 10 = 10
  X = 10  ->  10 + 10 = 20
  IV = 4  ->  20 + 4 = 24
Final: \boxed{24}


### Task: unit
### Problem:
Convert 3 metres to centimetres.
### Reasoning:
<|cot_start|>Conversion factor: 1 metres = 100 centimetres.
So 3 metres = 3 * 100 centimetres.
Compute step by step:
  3 * 10^0 * 100 = 300
  running total = 300
Final: \boxed{300}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01001110 -> 00011011
  10000000 -> 11010101
  01011010 -> 00001111
Apply to: 11001011
### Reasoning:
<|cot_start|>Given examples:
  01001110 -> 00011011
  10000000 -> 11010101
  01011010 -> 00001111
Compare each bit position across the three examples:
  bit 0: 0,1,0 -> 0,1,0
  bit 1: 1,0,1 -> 0,1,0
  bit 2: 0,0,0 -> 0,0,0
  bit 3: 0,0,1 -> 1,1,0
  bit 4: 1,0,1 -> 1,0,1
  bit 5: 1,0,0 -> 0,1,1
  bit 6: 1,0,1 -> 1,0,1
  bit 7: 0,0,0 -> 1,1,1
Deduce rule: xor 0x55.
Apply to 11001011:
  result = 10011110
Final: \boxed{10011110}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01011111 -> 11110101
  00111011 -> 10010001
  11111010 -> 01010000
Apply to: 11110111
### Reasoning:
<|cot_start|>Given examples:
  01011111 -> 11110101
  00111011 -> 10010001
  11111010 -> 01010000
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 1,1,0
  bit 1: 1,0,1 -> 1,0,1
  bit 2: 0,1,1 -> 1,0,0
  bit 3: 1,1,1 -> 1,1,1
  bit 4: 1,1,1 -> 0,0,0
  bit 5: 1,0,0 -> 1,0,0
  bit 6: 1,1,1 -> 0,0,0
  bit 7: 1,1,0 -> 1,1,0
Deduce rule: xor 0xAA.
Apply to 11110111:
  result = 01011101
Final: \boxed{01011101}


### Task: gravity
### Problem:
A mass of 13 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 = 13 * 981.
Step-by-step multiplication:
  1 * 10^1 * 981 = 9810
  running total = 9810
  3 * 10^0 * 981 = 2943
  running total = 12753
So F = 12753 centiNewtons = 127.53 N.
Final: \boxed{127.53}


### Task: unit
### Problem:
Convert 84 days to hours.
### Reasoning:
<|cot_start|>Conversion factor: 1 days = 24 hours.
So 84 days = 84 * 24 hours.
Compute step by step:
  8 * 10^1 * 24 = 1920
  running total = 1920
  4 * 10^0 * 24 = 96
  running total = 2016
Final: \boxed{2016}


### Task: unit
### Problem:
Convert 55 kilograms to grams.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilograms = 1000 grams.
So 55 kilograms = 55 * 1000 grams.
Compute step by step:
  5 * 10^1 * 1000 = 50000
  running total = 50000
  5 * 10^0 * 1000 = 5000
  running total = 55000
Final: \boxed{55000}


### Task: numeral
### Problem:
Convert the Roman numeral LIV to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  IV = 4  ->  50 + 4 = 54
Final: \boxed{54}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  22,50 -> 5022
  29,43 -> 4329
  32,53 -> 5332
Apply to: 67,20
### Reasoning:
<|cot_start|>Examples:
  22,50 -> 5022
  29,43 -> 4329
  32,53 -> 5332
Check both candidate forms:
  concat(22,50)=2250  rev_concat(22,50)=5022  target=5022  rev_concat
  concat(29,43)=2943  rev_concat(29,43)=4329  target=4329  rev_concat
  concat(32,53)=3253  rev_concat(32,53)=5332  target=5332  rev_concat
Conclude operator: rev_concat.
Apply to (67, 20):  answer = 2067
Final: \boxed{2067}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  47,98 -> 9847
  64,23 -> 2364
  49,44 -> 4449
Apply to: 30,29
### Reasoning:
<|cot_start|>Examples:
  47,98 -> 9847
  64,23 -> 2364
  49,44 -> 4449
Check both candidate forms:
  concat(47,98)=4798  rev_concat(47,98)=9847  target=9847  rev_concat
  concat(64,23)=6423  rev_concat(64,23)=2364  target=2364  rev_concat
  concat(49,44)=4944  rev_concat(49,44)=4449  target=4449  rev_concat
Conclude operator: rev_concat.
Apply to (30, 29):  answer = 2930
Final: \boxed{2930}


### 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: unit
### Problem:
Convert 46 litres to millilitres.
### Reasoning:
<|cot_start|>Conversion factor: 1 litres = 1000 millilitres.
So 46 litres = 46 * 1000 millilitres.
Compute step by step:
  4 * 10^1 * 1000 = 40000
  running total = 40000
  6 * 10^0 * 1000 = 6000
  running total = 46000
Final: \boxed{46000}


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