### Task: equation
### Problem:
Discover the operator from examples then apply it:
  99,44 -> 9944
  53,90 -> 5390
  32,92 -> 3292
Apply to: 61,43
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  99,44: '+' gives 143; target=9944  no
  99,44: '-' gives 55; target=9944  no
  99,44: '*' gives 4356; target=9944  no
  99,44: 'concat' gives 9944; target=9944  MATCH
  99,44: 'rev_concat' gives 4499; target=9944  no
  99,44: 'max*min+sum' gives 4499; target=9944  no
  99,44: 'digitsum2' gives 676; target=9944  no
  53,90: '+' gives 143; target=5390  no
  53,90: '-' gives 37; target=5390  no
  53,90: '*' gives 4770; target=5390  no
  53,90: 'concat' gives 5390; target=5390  MATCH
  53,90: 'rev_concat' gives 9053; target=5390  no
  53,90: 'max*min+sum' gives 4913; target=5390  no
  53,90: 'digitsum2' gives 289; target=5390  no
  32,92: '+' gives 124; target=3292  no
  32,92: '-' gives 60; target=3292  no
  32,92: '*' gives 2944; target=3292  no
  32,92: 'concat' gives 3292; target=3292  MATCH
  32,92: 'rev_concat' gives 9232; target=3292  no
  32,92: 'max*min+sum' gives 3068; target=3292  no
  32,92: 'digitsum2' gives 256; target=3292  no
The only operator consistent with all examples is 'concat'.
Apply to (61, 43):
  result = 6143
Final: \boxed{6143}


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


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00000010 -> 01010111
  00110110 -> 01100011
  10101000 -> 11111101
Apply to: 01101010
### Reasoning:
<|cot_start|>Given examples:
  00000010 -> 01010111
  00110110 -> 01100011
  10101000 -> 11111101
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 0,0,1
  bit 1: 0,0,0 -> 1,1,1
  bit 2: 0,1,1 -> 0,1,1
  bit 3: 0,1,0 -> 1,0,1
  bit 4: 0,0,1 -> 0,0,1
  bit 5: 0,1,0 -> 1,0,1
  bit 6: 1,1,0 -> 1,1,0
  bit 7: 0,0,0 -> 1,1,1
Deduce rule: xor 0x55.
Apply to 01101010:
  result = 00111111
Final: \boxed{00111111}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  94,23 -> 9423
  43,65 -> 4365
  92,22 -> 9222
Apply to: 14,22
### Reasoning:
<|cot_start|>Examples:
  94,23 -> 9423
  43,65 -> 4365
  92,22 -> 9222
Check both candidate forms:
  concat(94,23)=9423  rev_concat(94,23)=2394  target=9423  concat
  concat(43,65)=4365  rev_concat(43,65)=6543  target=4365  concat
  concat(92,22)=9222  rev_concat(92,22)=2292  target=9222  concat
Conclude operator: concat.
Apply to (14, 22):  answer = 1422
Final: \boxed{1422}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  89,90 -> 676
  30,28 -> 169
  81,82 -> 361
Apply to: 53,97
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  89,90: '+' gives 179; target=676  no
  89,90: '-' gives 1; target=676  no
  89,90: '*' gives 8010; target=676  no
  89,90: 'concat' gives 8990; target=676  no
  89,90: 'rev_concat' gives 9089; target=676  no
  89,90: 'max*min+sum' gives 8189; target=676  no
  89,90: 'digitsum2' gives 676; target=676  MATCH
  30,28: '+' gives 58; target=169  no
  30,28: '-' gives 2; target=169  no
  30,28: '*' gives 840; target=169  no
  30,28: 'concat' gives 3028; target=169  no
  30,28: 'rev_concat' gives 2830; target=169  no
  30,28: 'max*min+sum' gives 898; target=169  no
  30,28: 'digitsum2' gives 169; target=169  MATCH
  81,82: '+' gives 163; target=361  no
  81,82: '-' gives 1; target=361  no
  81,82: '*' gives 6642; target=361  no
  81,82: 'concat' gives 8182; target=361  no
  81,82: 'rev_concat' gives 8281; target=361  no
  81,82: 'max*min+sum' gives 6805; target=361  no
  81,82: 'digitsum2' gives 361; target=361  MATCH
The only operator consistent with all examples is 'digitsum2'.
Apply to (53, 97):
  result = 576
Final: \boxed{576}


### Task: numeral
### Problem:
Convert the Roman numeral LXXV 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
Final: \boxed{75}


### Task: numeral
### Problem:
Convert the Roman numeral XVIII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  X = 10  ->  0 + 10 = 10
  V = 5  ->  10 + 5 = 15
  I = 1  ->  15 + 1 = 16
  I = 1  ->  16 + 1 = 17
  I = 1  ->  17 + 1 = 18
Final: \boxed{18}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  94,31 -> 3194
  37,59 -> 5937
  65,35 -> 3565
Apply to: 36,11
### Reasoning:
<|cot_start|>Examples:
  94,31 -> 3194
  37,59 -> 5937
  65,35 -> 3565
Check both candidate forms:
  concat(94,31)=9431  rev_concat(94,31)=3194  target=3194  rev_concat
  concat(37,59)=3759  rev_concat(37,59)=5937  target=5937  rev_concat
  concat(65,35)=6535  rev_concat(65,35)=3565  target=3565  rev_concat
Conclude operator: rev_concat.
Apply to (36, 11):  answer = 1136
Final: \boxed{1136}


### Task: numeral
### Problem:
Convert the Roman numeral XXXIX 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
  IX = 9  ->  30 + 9 = 39
Final: \boxed{39}


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


### Task: unit
### Problem:
Convert 15 minutes to seconds.
### Reasoning:
<|cot_start|>Conversion factor: 1 minutes = 60 seconds.
So 15 minutes = 15 * 60 seconds.
Compute step by step:
  1 * 10^1 * 60 = 600
  running total = 600
  5 * 10^0 * 60 = 300
  running total = 900
Final: \boxed{900}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  88,65 -> 729
  68,93 -> 676
  67,60 -> 361
Apply to: 11,88
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  88,65: '+' gives 153; target=729  no
  88,65: '-' gives 23; target=729  no
  88,65: '*' gives 5720; target=729  no
  88,65: 'concat' gives 8865; target=729  no
  88,65: 'rev_concat' gives 6588; target=729  no
  88,65: 'max*min+sum' gives 5873; target=729  no
  88,65: 'digitsum2' gives 729; target=729  MATCH
  68,93: '+' gives 161; target=676  no
  68,93: '-' gives 25; target=676  no
  68,93: '*' gives 6324; target=676  no
  68,93: 'concat' gives 6893; target=676  no
  68,93: 'rev_concat' gives 9368; target=676  no
  68,93: 'max*min+sum' gives 6485; target=676  no
  68,93: 'digitsum2' gives 676; target=676  MATCH
  67,60: '+' gives 127; target=361  no
  67,60: '-' gives 7; target=361  no
  67,60: '*' gives 4020; target=361  no
  67,60: 'concat' gives 6760; target=361  no
  67,60: 'rev_concat' gives 6067; target=361  no
  67,60: 'max*min+sum' gives 4147; target=361  no
  67,60: 'digitsum2' gives 361; target=361  MATCH
The only operator consistent with all examples is 'digitsum2'.
Apply to (11, 88):
  result = 324
Final: \boxed{324}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  16,76 -> 7616
  77,72 -> 7277
  19,39 -> 3919
Apply to: 26,60
### Reasoning:
<|cot_start|>Examples:
  16,76 -> 7616
  77,72 -> 7277
  19,39 -> 3919
Check both candidate forms:
  concat(16,76)=1676  rev_concat(16,76)=7616  target=7616  rev_concat
  concat(77,72)=7772  rev_concat(77,72)=7277  target=7277  rev_concat
  concat(19,39)=1939  rev_concat(19,39)=3919  target=3919  rev_concat
Conclude operator: rev_concat.
Apply to (26, 60):  answer = 6026
Final: \boxed{6026}


### Task: gravity
### Problem:
A mass of 17 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 = 17 * 981.
Step-by-step multiplication:
  1 * 10^1 * 981 = 9810
  running total = 9810
  7 * 10^0 * 981 = 6867
  running total = 16677
So F = 16677 centiNewtons = 166.77 N.
Final: \boxed{166.77}


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


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  78,39 -> 7839
  18,48 -> 1848
  78,74 -> 7874
Apply to: 40,53
### Reasoning:
<|cot_start|>Examples:
  78,39 -> 7839
  18,48 -> 1848
  78,74 -> 7874
Check both candidate forms:
  concat(78,39)=7839  rev_concat(78,39)=3978  target=7839  concat
  concat(18,48)=1848  rev_concat(18,48)=4818  target=1848  concat
  concat(78,74)=7874  rev_concat(78,74)=7478  target=7874  concat
Conclude operator: concat.
Apply to (40, 53):  answer = 4053
Final: \boxed{4053}


### Task: unit
### Problem:
Convert 78 metres to centimetres.
### Reasoning:
<|cot_start|>Conversion factor: 1 metres = 100 centimetres.
So 78 metres = 78 * 100 centimetres.
Compute step by step:
  7 * 10^1 * 100 = 7000
  running total = 7000
  8 * 10^0 * 100 = 800
  running total = 7800
Final: \boxed{7800}


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


### Task: numeral
### Problem:
Convert the Roman numeral XXXVII 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
  V = 5  ->  30 + 5 = 35
  I = 1  ->  35 + 1 = 36
  I = 1  ->  36 + 1 = 37
Final: \boxed{37}


### Task: gravity
### Problem:
A mass of 10 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 = 10 * 981.
Step-by-step multiplication:
  1 * 10^1 * 981 = 9810
  running total = 9810
  0 * 10^0 * 981 = 0
  running total = 9810
So F = 9810 centiNewtons = 98.10 N.
Final: \boxed{98.10}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  53,90 -> 5390
  45,39 -> 4539
  60,10 -> 6010
Apply to: 17,97
### Reasoning:
<|cot_start|>Examples:
  53,90 -> 5390
  45,39 -> 4539
  60,10 -> 6010
Check both candidate forms:
  concat(53,90)=5390  rev_concat(53,90)=9053  target=5390  concat
  concat(45,39)=4539  rev_concat(45,39)=3945  target=4539  concat
  concat(60,10)=6010  rev_concat(60,10)=1060  target=6010  concat
Conclude operator: concat.
Apply to (17, 97):  answer = 1797
Final: \boxed{1797}


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


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11000101 -> 11110101
  11110101 -> 11110101
  01111001 -> 11111001
Apply to: 11001001
### Reasoning:
<|cot_start|>Given examples:
  11000101 -> 11110101
  11110101 -> 11110101
  01111001 -> 11111001
Compare each bit position across the three examples:
  bit 0: 1,1,0 -> 1,1,1
  bit 1: 1,1,1 -> 1,1,1
  bit 2: 0,1,1 -> 1,1,1
  bit 3: 0,1,1 -> 1,1,1
  bit 4: 0,0,1 -> 0,0,1
  bit 5: 1,1,0 -> 1,1,0
  bit 6: 0,0,0 -> 0,0,0
  bit 7: 1,1,1 -> 1,1,1
Deduce rule: or 0xF0.
Apply to 11001001:
  result = 11111001
Final: \boxed{11111001}


### 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: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10001110 -> 01000111
  00111111 -> 10011111
  10101100 -> 01010110
Apply to: 00000000
### Reasoning:
<|cot_start|>Given examples:
  10001110 -> 01000111
  00111111 -> 10011111
  10101100 -> 01010110
Compare each bit position across the three examples:
  bit 0: 1,0,1 -> 0,1,0
  bit 1: 0,0,0 -> 1,0,1
  bit 2: 0,1,1 -> 0,0,0
  bit 3: 0,1,0 -> 0,1,1
  bit 4: 1,1,1 -> 0,1,0
  bit 5: 1,1,1 -> 1,1,1
  bit 6: 1,1,0 -> 1,1,1
  bit 7: 0,1,0 -> 1,1,0
Deduce rule: rotate right 1.
Apply to 00000000:
  result = 00000000
Final: \boxed{00000000}


### Task: numeral
### Problem:
Convert the Roman numeral XCI to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  XC = 90  ->  0 + 90 = 90
  I = 1  ->  90 + 1 = 91
Final: \boxed{91}


### 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: 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: numeral
### Problem:
Convert the Roman numeral LXIV to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  X = 10  ->  50 + 10 = 60
  IV = 4  ->  60 + 4 = 64
Final: \boxed{64}


### Task: numeral
### Problem:
Convert the Roman numeral XXXVIII 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
  V = 5  ->  30 + 5 = 35
  I = 1  ->  35 + 1 = 36
  I = 1  ->  36 + 1 = 37
  I = 1  ->  37 + 1 = 38
Final: \boxed{38}


### Task: gravity
### Problem:
A mass of 26 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 26 * 981.
Step-by-step multiplication:
  2 * 10^1 * 981 = 19620
  running total = 19620
  6 * 10^0 * 981 = 5886
  running total = 25506
So F = 25506 centiNewtons = 255.06 N.
Final: \boxed{255.06}


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


### Task: 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: gravity
### Problem:
A mass of 43 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 = 43 * 981.
Step-by-step multiplication:
  4 * 10^1 * 981 = 39240
  running total = 39240
  3 * 10^0 * 981 = 2943
  running total = 42183
So F = 42183 centiNewtons = 421.83 N.
Final: \boxed{421.83}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  45,99 -> 4599
  11,37 -> 1137
  69,48 -> 6948
Apply to: 61,64
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  45,99: '+' gives 144; target=4599  no
  45,99: '-' gives 54; target=4599  no
  45,99: '*' gives 4455; target=4599  no
  45,99: 'concat' gives 4599; target=4599  MATCH
  45,99: 'rev_concat' gives 9945; target=4599  no
  45,99: 'max*min+sum' gives 4599; target=4599  MATCH
  45,99: 'digitsum2' gives 729; target=4599  no
  11,37: '+' gives 48; target=1137  no
  11,37: '-' gives 26; target=1137  no
  11,37: '*' gives 407; target=1137  no
  11,37: 'concat' gives 1137; target=1137  MATCH
  11,37: 'rev_concat' gives 3711; target=1137  no
  11,37: 'max*min+sum' gives 455; target=1137  no
  11,37: 'digitsum2' gives 144; target=1137  no
  69,48: '+' gives 117; target=6948  no
  69,48: '-' gives 21; target=6948  no
  69,48: '*' gives 3312; target=6948  no
  69,48: 'concat' gives 6948; target=6948  MATCH
  69,48: 'rev_concat' gives 4869; target=6948  no
  69,48: 'max*min+sum' gives 3429; target=6948  no
  69,48: 'digitsum2' gives 729; target=6948  no
The only operator consistent with all examples is 'concat'.
Apply to (61, 64):
  result = 6164
Final: \boxed{6164}


### 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 92 metres to centimetres.
### Reasoning:
<|cot_start|>Conversion factor: 1 metres = 100 centimetres.
So 92 metres = 92 * 100 centimetres.
Compute step by step:
  9 * 10^1 * 100 = 9000
  running total = 9000
  2 * 10^0 * 100 = 200
  running total = 9200
Final: \boxed{9200}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  61,91 -> 6191
  37,21 -> 3721
  63,44 -> 6344
Apply to: 72,65
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  61,91: '+' gives 152; target=6191  no
  61,91: '-' gives 30; target=6191  no
  61,91: '*' gives 5551; target=6191  no
  61,91: 'concat' gives 6191; target=6191  MATCH
  61,91: 'rev_concat' gives 9161; target=6191  no
  61,91: 'max*min+sum' gives 5703; target=6191  no
  61,91: 'digitsum2' gives 289; target=6191  no
  37,21: '+' gives 58; target=3721  no
  37,21: '-' gives 16; target=3721  no
  37,21: '*' gives 777; target=3721  no
  37,21: 'concat' gives 3721; target=3721  MATCH
  37,21: 'rev_concat' gives 2137; target=3721  no
  37,21: 'max*min+sum' gives 835; target=3721  no
  37,21: 'digitsum2' gives 169; target=3721  no
  63,44: '+' gives 107; target=6344  no
  63,44: '-' gives 19; target=6344  no
  63,44: '*' gives 2772; target=6344  no
  63,44: 'concat' gives 6344; target=6344  MATCH
  63,44: 'rev_concat' gives 4463; target=6344  no
  63,44: 'max*min+sum' gives 2879; target=6344  no
  63,44: 'digitsum2' gives 289; target=6344  no
The only operator consistent with all examples is 'concat'.
Apply to (72, 65):
  result = 7265
Final: \boxed{7265}


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


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  35,25 -> 60
  47,51 -> 98
  52,49 -> 101
Apply to: 28,33
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  35,25: '+' gives 60; target=60  MATCH
  35,25: '-' gives 10; target=60  no
  35,25: '*' gives 875; target=60  no
  35,25: 'concat' gives 3525; target=60  no
  35,25: 'rev_concat' gives 2535; target=60  no
  35,25: 'max*min+sum' gives 935; target=60  no
  35,25: 'digitsum2' gives 225; target=60  no
  47,51: '+' gives 98; target=98  MATCH
  47,51: '-' gives 4; target=98  no
  47,51: '*' gives 2397; target=98  no
  47,51: 'concat' gives 4751; target=98  no
  47,51: 'rev_concat' gives 5147; target=98  no
  47,51: 'max*min+sum' gives 2495; target=98  no
  47,51: 'digitsum2' gives 289; target=98  no
  52,49: '+' gives 101; target=101  MATCH
  52,49: '-' gives 3; target=101  no
  52,49: '*' gives 2548; target=101  no
  52,49: 'concat' gives 5249; target=101  no
  52,49: 'rev_concat' gives 4952; target=101  no
  52,49: 'max*min+sum' gives 2649; target=101  no
  52,49: 'digitsum2' gives 400; target=101  no
The only operator consistent with all examples is '+'.
Apply to (28, 33):
  result = 61
Final: \boxed{61}


### Task: numeral
### Problem:
Convert the Roman numeral LXXIV 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
  IV = 4  ->  70 + 4 = 74
Final: \boxed{74}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  16,69 -> 1669
  71,80 -> 7180
  80,40 -> 8040
Apply to: 64,41
### Reasoning:
<|cot_start|>Examples:
  16,69 -> 1669
  71,80 -> 7180
  80,40 -> 8040
Check both candidate forms:
  concat(16,69)=1669  rev_concat(16,69)=6916  target=1669  concat
  concat(71,80)=7180  rev_concat(71,80)=8071  target=7180  concat
  concat(80,40)=8040  rev_concat(80,40)=4080  target=8040  concat
Conclude operator: concat.
Apply to (64, 41):  answer = 6441
Final: \boxed{6441}


### Task: unit
### Problem:
Convert 91 kilometres to metres.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilometres = 1000 metres.
So 91 kilometres = 91 * 1000 metres.
Compute step by step:
  9 * 10^1 * 1000 = 90000
  running total = 90000
  1 * 10^0 * 1000 = 1000
  running total = 91000
Final: \boxed{91000}


### Task: gravity
### Problem:
A mass of 12 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 = 12 * 981.
Step-by-step multiplication:
  1 * 10^1 * 981 = 9810
  running total = 9810
  2 * 10^0 * 981 = 1962
  running total = 11772
So F = 11772 centiNewtons = 117.72 N.
Final: \boxed{117.72}


### Task: unit
### Problem:
Convert 34 days to hours.
### Reasoning:
<|cot_start|>Conversion factor: 1 days = 24 hours.
So 34 days = 34 * 24 hours.
Compute step by step:
  3 * 10^1 * 24 = 720
  running total = 720
  4 * 10^0 * 24 = 96
  running total = 816
Final: \boxed{816}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  25,29 -> 2925
  80,40 -> 4080
  39,71 -> 7139
Apply to: 87,43
### Reasoning:
<|cot_start|>Examples:
  25,29 -> 2925
  80,40 -> 4080
  39,71 -> 7139
Check both candidate forms:
  concat(25,29)=2529  rev_concat(25,29)=2925  target=2925  rev_concat
  concat(80,40)=8040  rev_concat(80,40)=4080  target=4080  rev_concat
  concat(39,71)=3971  rev_concat(39,71)=7139  target=7139  rev_concat
Conclude operator: rev_concat.
Apply to (87, 43):  answer = 4387
Final: \boxed{4387}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  14,64 -> 6414
  13,83 -> 8313
  90,80 -> 8090
Apply to: 12,16
### Reasoning:
<|cot_start|>Examples:
  14,64 -> 6414
  13,83 -> 8313
  90,80 -> 8090
Check both candidate forms:
  concat(14,64)=1464  rev_concat(14,64)=6414  target=6414  rev_concat
  concat(13,83)=1383  rev_concat(13,83)=8313  target=8313  rev_concat
  concat(90,80)=9080  rev_concat(90,80)=8090  target=8090  rev_concat
Conclude operator: rev_concat.
Apply to (12, 16):  answer = 1612
Final: \boxed{1612}


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


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00101101 -> 01011010
  01001001 -> 10010010
  01111110 -> 11111100
Apply to: 01101101
### Reasoning:
<|cot_start|>Given examples:
  00101101 -> 01011010
  01001001 -> 10010010
  01111110 -> 11111100
Compare each bit position across the three examples:
  bit 0: 0,0,0 -> 0,1,1
  bit 1: 0,1,1 -> 1,0,1
  bit 2: 1,0,1 -> 0,0,1
  bit 3: 0,0,1 -> 1,1,1
  bit 4: 1,1,1 -> 1,0,1
  bit 5: 1,0,1 -> 0,0,1
  bit 6: 0,0,1 -> 1,1,0
  bit 7: 1,1,0 -> 0,0,0
Deduce rule: rotate left 1.
Apply to 01101101:
  result = 11011010
Final: \boxed{11011010}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  57,44 -> 4457
  94,55 -> 5594
  29,62 -> 6229
Apply to: 36,35
### Reasoning:
<|cot_start|>Examples:
  57,44 -> 4457
  94,55 -> 5594
  29,62 -> 6229
Check both candidate forms:
  concat(57,44)=5744  rev_concat(57,44)=4457  target=4457  rev_concat
  concat(94,55)=9455  rev_concat(94,55)=5594  target=5594  rev_concat
  concat(29,62)=2962  rev_concat(29,62)=6229  target=6229  rev_concat
Conclude operator: rev_concat.
Apply to (36, 35):  answer = 3536
Final: \boxed{3536}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11111110 -> 01010100
  10001001 -> 00100011
  01011000 -> 11110010
Apply to: 00000111
### Reasoning:
<|cot_start|>Given examples:
  11111110 -> 01010100
  10001001 -> 00100011
  01011000 -> 11110010
Compare each bit position across the three examples:
  bit 0: 1,1,0 -> 0,0,1
  bit 1: 1,0,1 -> 1,0,1
  bit 2: 1,0,0 -> 0,1,1
  bit 3: 1,0,1 -> 1,0,1
  bit 4: 1,1,1 -> 0,0,0
  bit 5: 1,0,0 -> 1,0,0
  bit 6: 1,0,0 -> 0,1,1
  bit 7: 0,1,0 -> 0,1,0
Deduce rule: xor 0xAA.
Apply to 00000111:
  result = 10101101
Final: \boxed{10101101}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00001100 -> 00110000
  10101101 -> 10110101
  01001111 -> 11110010
Apply to: 01011101
### Reasoning:
<|cot_start|>Given examples:
  00001100 -> 00110000
  10101101 -> 10110101
  01001111 -> 11110010
Compare each bit position across the three examples:
  bit 0: 0,1,0 -> 0,1,1
  bit 1: 0,0,1 -> 0,0,1
  bit 2: 0,1,0 -> 1,1,1
  bit 3: 0,0,0 -> 1,1,1
  bit 4: 1,1,1 -> 0,0,0
  bit 5: 1,1,1 -> 0,1,0
  bit 6: 0,0,1 -> 0,0,1
  bit 7: 0,1,1 -> 0,1,0
Deduce rule: reverse bits.
Apply to 01011101:
  result = 10111010
Final: \boxed{10111010}


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


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


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  37,75 -> 38
  61,72 -> 11
  38,83 -> 45
Apply to: 20,79
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  37,75: '+' gives 112; target=38  no
  37,75: '-' gives 38; target=38  MATCH
  37,75: '*' gives 2775; target=38  no
  37,75: 'concat' gives 3775; target=38  no
  37,75: 'rev_concat' gives 7537; target=38  no
  37,75: 'max*min+sum' gives 2887; target=38  no
  37,75: 'digitsum2' gives 484; target=38  no
  61,72: '+' gives 133; target=11  no
  61,72: '-' gives 11; target=11  MATCH
  61,72: '*' gives 4392; target=11  no
  61,72: 'concat' gives 6172; target=11  no
  61,72: 'rev_concat' gives 7261; target=11  no
  61,72: 'max*min+sum' gives 4525; target=11  no
  61,72: 'digitsum2' gives 256; target=11  no
  38,83: '+' gives 121; target=45  no
  38,83: '-' gives 45; target=45  MATCH
  38,83: '*' gives 3154; target=45  no
  38,83: 'concat' gives 3883; target=45  no
  38,83: 'rev_concat' gives 8338; target=45  no
  38,83: 'max*min+sum' gives 3275; target=45  no
  38,83: 'digitsum2' gives 484; target=45  no
The only operator consistent with all examples is '-'.
Apply to (20, 79):
  result = 59
Final: \boxed{59}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  26,42 -> 4226
  83,46 -> 4683
  46,33 -> 3346
Apply to: 17,45
### Reasoning:
<|cot_start|>Examples:
  26,42 -> 4226
  83,46 -> 4683
  46,33 -> 3346
Check both candidate forms:
  concat(26,42)=2642  rev_concat(26,42)=4226  target=4226  rev_concat
  concat(83,46)=8346  rev_concat(83,46)=4683  target=4683  rev_concat
  concat(46,33)=4633  rev_concat(46,33)=3346  target=3346  rev_concat
Conclude operator: rev_concat.
Apply to (17, 45):  answer = 4517
Final: \boxed{4517}


### Task: unit
### Problem:
Convert 9 hours to minutes.
### Reasoning:
<|cot_start|>Conversion factor: 1 hours = 60 minutes.
So 9 hours = 9 * 60 minutes.
Compute step by step:
  9 * 10^0 * 60 = 540
  running total = 540
Final: \boxed{540}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  17,63 -> 1763
  64,52 -> 6452
  64,58 -> 6458
Apply to: 15,44
### Reasoning:
<|cot_start|>Examples:
  17,63 -> 1763
  64,52 -> 6452
  64,58 -> 6458
Check both candidate forms:
  concat(17,63)=1763  rev_concat(17,63)=6317  target=1763  concat
  concat(64,52)=6452  rev_concat(64,52)=5264  target=6452  concat
  concat(64,58)=6458  rev_concat(64,58)=5864  target=6458  concat
Conclude operator: concat.
Apply to (15, 44):  answer = 1544
Final: \boxed{1544}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  43,55 -> 2365
  85,42 -> 3570
  66,76 -> 5016
Apply to: 14,49
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  43,55: '+' gives 98; target=2365  no
  43,55: '-' gives 12; target=2365  no
  43,55: '*' gives 2365; target=2365  MATCH
  43,55: 'concat' gives 4355; target=2365  no
  43,55: 'rev_concat' gives 5543; target=2365  no
  43,55: 'max*min+sum' gives 2463; target=2365  no
  43,55: 'digitsum2' gives 289; target=2365  no
  85,42: '+' gives 127; target=3570  no
  85,42: '-' gives 43; target=3570  no
  85,42: '*' gives 3570; target=3570  MATCH
  85,42: 'concat' gives 8542; target=3570  no
  85,42: 'rev_concat' gives 4285; target=3570  no
  85,42: 'max*min+sum' gives 3697; target=3570  no
  85,42: 'digitsum2' gives 361; target=3570  no
  66,76: '+' gives 142; target=5016  no
  66,76: '-' gives 10; target=5016  no
  66,76: '*' gives 5016; target=5016  MATCH
  66,76: 'concat' gives 6676; target=5016  no
  66,76: 'rev_concat' gives 7666; target=5016  no
  66,76: 'max*min+sum' gives 5158; target=5016  no
  66,76: 'digitsum2' gives 625; target=5016  no
The only operator consistent with all examples is '*'.
Apply to (14, 49):
  result = 686
Final: \boxed{686}


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


### Task: unit
### Problem:
Convert 94 kilograms to grams.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilograms = 1000 grams.
So 94 kilograms = 94 * 1000 grams.
Compute step by step:
  9 * 10^1 * 1000 = 90000
  running total = 90000
  4 * 10^0 * 1000 = 4000
  running total = 94000
Final: \boxed{94000}


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


### Task: unit
### Problem:
Convert 37 minutes to seconds.
### Reasoning:
<|cot_start|>Conversion factor: 1 minutes = 60 seconds.
So 37 minutes = 37 * 60 seconds.
Compute step by step:
  3 * 10^1 * 60 = 1800
  running total = 1800
  7 * 10^0 * 60 = 420
  running total = 2220
Final: \boxed{2220}


### 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: numeral
### Problem:
Convert the Roman numeral XXXIX 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
  IX = 9  ->  30 + 9 = 39
Final: \boxed{39}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  47,10 -> 4710
  32,98 -> 3298
  83,68 -> 8368
Apply to: 78,18
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  47,10: '+' gives 57; target=4710  no
  47,10: '-' gives 37; target=4710  no
  47,10: '*' gives 470; target=4710  no
  47,10: 'concat' gives 4710; target=4710  MATCH
  47,10: 'rev_concat' gives 1047; target=4710  no
  47,10: 'max*min+sum' gives 527; target=4710  no
  47,10: 'digitsum2' gives 144; target=4710  no
  32,98: '+' gives 130; target=3298  no
  32,98: '-' gives 66; target=3298  no
  32,98: '*' gives 3136; target=3298  no
  32,98: 'concat' gives 3298; target=3298  MATCH
  32,98: 'rev_concat' gives 9832; target=3298  no
  32,98: 'max*min+sum' gives 3266; target=3298  no
  32,98: 'digitsum2' gives 484; target=3298  no
  83,68: '+' gives 151; target=8368  no
  83,68: '-' gives 15; target=8368  no
  83,68: '*' gives 5644; target=8368  no
  83,68: 'concat' gives 8368; target=8368  MATCH
  83,68: 'rev_concat' gives 6883; target=8368  no
  83,68: 'max*min+sum' gives 5795; target=8368  no
  83,68: 'digitsum2' gives 625; target=8368  no
The only operator consistent with all examples is 'concat'.
Apply to (78, 18):
  result = 7818
Final: \boxed{7818}


### Task: numeral
### Problem:
Convert the Roman numeral XCI to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  XC = 90  ->  0 + 90 = 90
  I = 1  ->  90 + 1 = 91
Final: \boxed{91}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10001010 -> 11111010
  01010001 -> 11110001
  10000110 -> 11110110
Apply to: 00010111
### Reasoning:
<|cot_start|>Given examples:
  10001010 -> 11111010
  01010001 -> 11110001
  10000110 -> 11110110
Compare each bit position across the three examples:
  bit 0: 1,0,1 -> 1,1,1
  bit 1: 0,1,0 -> 1,1,1
  bit 2: 0,0,0 -> 1,1,1
  bit 3: 0,1,0 -> 1,1,1
  bit 4: 1,0,0 -> 1,0,0
  bit 5: 0,0,1 -> 0,0,1
  bit 6: 1,0,1 -> 1,0,1
  bit 7: 0,1,0 -> 0,1,0
Deduce rule: or 0xF0.
Apply to 00010111:
  result = 11110111
Final: \boxed{11110111}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11111000 -> 11110001
  11110001 -> 11100011
  10000111 -> 00001111
Apply to: 11001110
### Reasoning:
<|cot_start|>Given examples:
  11111000 -> 11110001
  11110001 -> 11100011
  10000111 -> 00001111
Compare each bit position across the three examples:
  bit 0: 1,1,1 -> 1,1,0
  bit 1: 1,1,0 -> 1,1,0
  bit 2: 1,1,0 -> 1,1,0
  bit 3: 1,1,0 -> 1,0,0
  bit 4: 1,0,0 -> 0,0,1
  bit 5: 0,0,1 -> 0,0,1
  bit 6: 0,0,1 -> 0,1,1
  bit 7: 0,1,1 -> 1,1,1
Deduce rule: rotate left 1.
Apply to 11001110:
  result = 10011101
Final: \boxed{10011101}


### Task: unit
### Problem:
Convert 6 metres to centimetres.
### Reasoning:
<|cot_start|>Conversion factor: 1 metres = 100 centimetres.
So 6 metres = 6 * 100 centimetres.
Compute step by step:
  6 * 10^0 * 100 = 600
  running total = 600
Final: \boxed{600}


### Task: gravity
### Problem:
A mass of 46 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 = 46 * 981.
Step-by-step multiplication:
  4 * 10^1 * 981 = 39240
  running total = 39240
  6 * 10^0 * 981 = 5886
  running total = 45126
So F = 45126 centiNewtons = 451.26 N.
Final: \boxed{451.26}


### Task: numeral
### Problem:
Convert the Roman numeral LXII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  X = 10  ->  50 + 10 = 60
  I = 1  ->  60 + 1 = 61
  I = 1  ->  61 + 1 = 62
Final: \boxed{62}


### Task: gravity
### Problem:
A mass of 31 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 = 31 * 981.
Step-by-step multiplication:
  3 * 10^1 * 981 = 29430
  running total = 29430
  1 * 10^0 * 981 = 981
  running total = 30411
So F = 30411 centiNewtons = 304.11 N.
Final: \boxed{304.11}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  50,13 -> 1350
  96,69 -> 6996
  75,39 -> 3975
Apply to: 43,58
### Reasoning:
<|cot_start|>Examples:
  50,13 -> 1350
  96,69 -> 6996
  75,39 -> 3975
Check both candidate forms:
  concat(50,13)=5013  rev_concat(50,13)=1350  target=1350  rev_concat
  concat(96,69)=9669  rev_concat(96,69)=6996  target=6996  rev_concat
  concat(75,39)=7539  rev_concat(75,39)=3975  target=3975  rev_concat
Conclude operator: rev_concat.
Apply to (43, 58):  answer = 5843
Final: \boxed{5843}


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


### Task: numeral
### Problem:
Convert the Roman numeral XCIII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  XC = 90  ->  0 + 90 = 90
  I = 1  ->  90 + 1 = 91
  I = 1  ->  91 + 1 = 92
  I = 1  ->  92 + 1 = 93
Final: \boxed{93}


### Task: numeral
### Problem:
Convert the Roman numeral XXV 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
Final: \boxed{25}


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


### Task: unit
### Problem:
Convert 83 kilometres to metres.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilometres = 1000 metres.
So 83 kilometres = 83 * 1000 metres.
Compute step by step:
  8 * 10^1 * 1000 = 80000
  running total = 80000
  3 * 10^0 * 1000 = 3000
  running total = 83000
Final: \boxed{83000}


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


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  33,67 -> 6733
  43,32 -> 3243
  14,56 -> 5614
Apply to: 96,47
### Reasoning:
<|cot_start|>Examples:
  33,67 -> 6733
  43,32 -> 3243
  14,56 -> 5614
Check both candidate forms:
  concat(33,67)=3367  rev_concat(33,67)=6733  target=6733  rev_concat
  concat(43,32)=4332  rev_concat(43,32)=3243  target=3243  rev_concat
  concat(14,56)=1456  rev_concat(14,56)=5614  target=5614  rev_concat
Conclude operator: rev_concat.
Apply to (96, 47):  answer = 4796
Final: \boxed{4796}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10010110 -> 01101001
  10011110 -> 01100001
  00011101 -> 11100010
Apply to: 00000000
### Reasoning:
<|cot_start|>Given examples:
  10010110 -> 01101001
  10011110 -> 01100001
  00011101 -> 11100010
Compare each bit position across the three examples:
  bit 0: 1,1,0 -> 0,0,1
  bit 1: 0,0,0 -> 1,1,1
  bit 2: 0,0,0 -> 1,1,1
  bit 3: 1,1,1 -> 0,0,0
  bit 4: 0,1,1 -> 1,0,0
  bit 5: 1,1,1 -> 0,0,0
  bit 6: 1,1,0 -> 0,0,1
  bit 7: 0,0,1 -> 1,1,0
Deduce rule: invert (NOT).
Apply to 00000000:
  result = 11111111
Final: \boxed{11111111}


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


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  88,47 -> 4788
  98,43 -> 4398
  72,10 -> 1072
Apply to: 67,30
### Reasoning:
<|cot_start|>Examples:
  88,47 -> 4788
  98,43 -> 4398
  72,10 -> 1072
Check both candidate forms:
  concat(88,47)=8847  rev_concat(88,47)=4788  target=4788  rev_concat
  concat(98,43)=9843  rev_concat(98,43)=4398  target=4398  rev_concat
  concat(72,10)=7210  rev_concat(72,10)=1072  target=1072  rev_concat
Conclude operator: rev_concat.
Apply to (67, 30):  answer = 3067
Final: \boxed{3067}


### 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: gravity
### Problem:
A mass of 9 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 = 9 * 981.
Step-by-step multiplication:
  9 * 10^0 * 981 = 8829
  running total = 8829
So F = 8829 centiNewtons = 88.29 N.
Final: \boxed{88.29}


### Task: gravity
### Problem:
A mass of 17 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 = 17 * 981.
Step-by-step multiplication:
  1 * 10^1 * 981 = 9810
  running total = 9810
  7 * 10^0 * 981 = 6867
  running total = 16677
So F = 16677 centiNewtons = 166.77 N.
Final: \boxed{166.77}


### Task: unit
### Problem:
Convert 34 metres to centimetres.
### Reasoning:
<|cot_start|>Conversion factor: 1 metres = 100 centimetres.
So 34 metres = 34 * 100 centimetres.
Compute step by step:
  3 * 10^1 * 100 = 3000
  running total = 3000
  4 * 10^0 * 100 = 400
  running total = 3400
Final: \boxed{3400}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00100001 -> 10010000
  01110100 -> 00111010
  10101001 -> 11010100
Apply to: 01110110
### Reasoning:
<|cot_start|>Given examples:
  00100001 -> 10010000
  01110100 -> 00111010
  10101001 -> 11010100
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 1,0,1
  bit 1: 0,1,0 -> 0,0,1
  bit 2: 1,1,1 -> 0,1,0
  bit 3: 0,1,0 -> 1,1,1
  bit 4: 0,0,1 -> 0,1,0
  bit 5: 0,1,0 -> 0,0,1
  bit 6: 0,0,0 -> 0,1,0
  bit 7: 1,0,1 -> 0,0,0
Deduce rule: rotate right 1.
Apply to 01110110:
  result = 00111011
Final: \boxed{00111011}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  92,24 -> 9224
  62,36 -> 6236
  53,21 -> 5321
Apply to: 23,27
### Reasoning:
<|cot_start|>Examples:
  92,24 -> 9224
  62,36 -> 6236
  53,21 -> 5321
Check both candidate forms:
  concat(92,24)=9224  rev_concat(92,24)=2492  target=9224  concat
  concat(62,36)=6236  rev_concat(62,36)=3662  target=6236  concat
  concat(53,21)=5321  rev_concat(53,21)=2153  target=5321  concat
Conclude operator: concat.
Apply to (23, 27):  answer = 2327
Final: \boxed{2327}


### Task: gravity
### Problem:
A mass of 34 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 = 34 * 981.
Step-by-step multiplication:
  3 * 10^1 * 981 = 29430
  running total = 29430
  4 * 10^0 * 981 = 3924
  running total = 33354
So F = 33354 centiNewtons = 333.54 N.
Final: \boxed{333.54}


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


### Task: numeral
### Problem:
Convert the Roman numeral LXX 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
Final: \boxed{70}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  96,82 -> 178
  41,78 -> 119
  18,37 -> 55
Apply to: 51,67
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  96,82: '+' gives 178; target=178  MATCH
  96,82: '-' gives 14; target=178  no
  96,82: '*' gives 7872; target=178  no
  96,82: 'concat' gives 9682; target=178  no
  96,82: 'rev_concat' gives 8296; target=178  no
  96,82: 'max*min+sum' gives 8050; target=178  no
  96,82: 'digitsum2' gives 625; target=178  no
  41,78: '+' gives 119; target=119  MATCH
  41,78: '-' gives 37; target=119  no
  41,78: '*' gives 3198; target=119  no
  41,78: 'concat' gives 4178; target=119  no
  41,78: 'rev_concat' gives 7841; target=119  no
  41,78: 'max*min+sum' gives 3317; target=119  no
  41,78: 'digitsum2' gives 400; target=119  no
  18,37: '+' gives 55; target=55  MATCH
  18,37: '-' gives 19; target=55  no
  18,37: '*' gives 666; target=55  no
  18,37: 'concat' gives 1837; target=55  no
  18,37: 'rev_concat' gives 3718; target=55  no
  18,37: 'max*min+sum' gives 721; target=55  no
  18,37: 'digitsum2' gives 361; target=55  no
The only operator consistent with all examples is '+'.
Apply to (51, 67):
  result = 118
Final: \boxed{118}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00001000 -> 01011101
  11010110 -> 10000011
  10111010 -> 11101111
Apply to: 01011111
### Reasoning:
<|cot_start|>Given examples:
  00001000 -> 01011101
  11010110 -> 10000011
  10111010 -> 11101111
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: 0,0,1 -> 0,0,1
  bit 3: 0,1,1 -> 1,0,0
  bit 4: 1,0,1 -> 1,0,1
  bit 5: 0,1,0 -> 1,0,1
  bit 6: 0,1,1 -> 0,1,1
  bit 7: 0,0,0 -> 1,1,1
Deduce rule: xor 0x55.
Apply to 01011111:
  result = 00001010
Final: \boxed{00001010}


### Task: unit
### Problem:
Convert 84 kilograms to grams.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilograms = 1000 grams.
So 84 kilograms = 84 * 1000 grams.
Compute step by step:
  8 * 10^1 * 1000 = 80000
  running total = 80000
  4 * 10^0 * 1000 = 4000
  running total = 84000
Final: \boxed{84000}


### 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: gravity
### Problem:
A mass of 6 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 6 * 981.
Step-by-step multiplication:
  6 * 10^0 * 981 = 5886
  running total = 5886
So F = 5886 centiNewtons = 58.86 N.
Final: \boxed{58.86}


### Task: unit
### Problem:
Convert 42 kilometres to metres.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilometres = 1000 metres.
So 42 kilometres = 42 * 1000 metres.
Compute step by step:
  4 * 10^1 * 1000 = 40000
  running total = 40000
  2 * 10^0 * 1000 = 2000
  running total = 42000
Final: \boxed{42000}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  63,42 -> 4263
  11,56 -> 5611
  27,15 -> 1527
Apply to: 75,37
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  63,42: '+' gives 105; target=4263  no
  63,42: '-' gives 21; target=4263  no
  63,42: '*' gives 2646; target=4263  no
  63,42: 'concat' gives 6342; target=4263  no
  63,42: 'rev_concat' gives 4263; target=4263  MATCH
  63,42: 'max*min+sum' gives 2751; target=4263  no
  63,42: 'digitsum2' gives 225; target=4263  no
  11,56: '+' gives 67; target=5611  no
  11,56: '-' gives 45; target=5611  no
  11,56: '*' gives 616; target=5611  no
  11,56: 'concat' gives 1156; target=5611  no
  11,56: 'rev_concat' gives 5611; target=5611  MATCH
  11,56: 'max*min+sum' gives 683; target=5611  no
  11,56: 'digitsum2' gives 169; target=5611  no
  27,15: '+' gives 42; target=1527  no
  27,15: '-' gives 12; target=1527  no
  27,15: '*' gives 405; target=1527  no
  27,15: 'concat' gives 2715; target=1527  no
  27,15: 'rev_concat' gives 1527; target=1527  MATCH
  27,15: 'max*min+sum' gives 447; target=1527  no
  27,15: 'digitsum2' gives 225; target=1527  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (75, 37):
  result = 3775
Final: \boxed{3775}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11010000 -> 10000101
  10010010 -> 11000111
  00010101 -> 01000000
Apply to: 10000100
### Reasoning:
<|cot_start|>Given examples:
  11010000 -> 10000101
  10010010 -> 11000111
  00010101 -> 01000000
Compare each bit position across the three examples:
  bit 0: 1,1,0 -> 1,1,0
  bit 1: 1,0,0 -> 0,1,1
  bit 2: 0,0,0 -> 0,0,0
  bit 3: 1,1,1 -> 0,0,0
  bit 4: 0,0,0 -> 0,0,0
  bit 5: 0,0,1 -> 1,1,0
  bit 6: 0,1,0 -> 0,1,0
  bit 7: 0,0,1 -> 1,1,0
Deduce rule: xor 0x55.
Apply to 10000100:
  result = 11010001
Final: \boxed{11010001}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  36,22 -> 3622
  48,48 -> 4848
  34,23 -> 3423
Apply to: 41,62
### Reasoning:
<|cot_start|>Examples:
  36,22 -> 3622
  48,48 -> 4848
  34,23 -> 3423
Check both candidate forms:
  concat(36,22)=3622  rev_concat(36,22)=2236  target=3622  concat
  concat(48,48)=4848  rev_concat(48,48)=4848  target=4848  concat
  concat(34,23)=3423  rev_concat(34,23)=2334  target=3423  concat
Conclude operator: concat.
Apply to (41, 62):  answer = 4162
Final: \boxed{4162}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  30,32 -> 960
  45,35 -> 1575
  25,55 -> 1375
Apply to: 58,29
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  30,32: '+' gives 62; target=960  no
  30,32: '-' gives 2; target=960  no
  30,32: '*' gives 960; target=960  MATCH
  30,32: 'concat' gives 3032; target=960  no
  30,32: 'rev_concat' gives 3230; target=960  no
  30,32: 'max*min+sum' gives 1022; target=960  no
  30,32: 'digitsum2' gives 64; target=960  no
  45,35: '+' gives 80; target=1575  no
  45,35: '-' gives 10; target=1575  no
  45,35: '*' gives 1575; target=1575  MATCH
  45,35: 'concat' gives 4535; target=1575  no
  45,35: 'rev_concat' gives 3545; target=1575  no
  45,35: 'max*min+sum' gives 1655; target=1575  no
  45,35: 'digitsum2' gives 289; target=1575  no
  25,55: '+' gives 80; target=1375  no
  25,55: '-' gives 30; target=1375  no
  25,55: '*' gives 1375; target=1375  MATCH
  25,55: 'concat' gives 2555; target=1375  no
  25,55: 'rev_concat' gives 5525; target=1375  no
  25,55: 'max*min+sum' gives 1455; target=1375  no
  25,55: 'digitsum2' gives 289; target=1375  no
The only operator consistent with all examples is '*'.
Apply to (58, 29):
  result = 1682
Final: \boxed{1682}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  94,83 -> 9483
  85,11 -> 8511
  21,14 -> 2114
Apply to: 29,88
### Reasoning:
<|cot_start|>Examples:
  94,83 -> 9483
  85,11 -> 8511
  21,14 -> 2114
Check both candidate forms:
  concat(94,83)=9483  rev_concat(94,83)=8394  target=9483  concat
  concat(85,11)=8511  rev_concat(85,11)=1185  target=8511  concat
  concat(21,14)=2114  rev_concat(21,14)=1421  target=2114  concat
Conclude operator: concat.
Apply to (29, 88):  answer = 2988
Final: \boxed{2988}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01011111 -> 11110101
  01110001 -> 11011011
  11101100 -> 01000110
Apply to: 10100101
### Reasoning:
<|cot_start|>Given examples:
  01011111 -> 11110101
  01110001 -> 11011011
  11101100 -> 01000110
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 1,1,0
  bit 1: 1,1,1 -> 1,1,1
  bit 2: 0,1,1 -> 1,0,0
  bit 3: 1,1,0 -> 1,1,0
  bit 4: 1,0,1 -> 0,1,0
  bit 5: 1,0,1 -> 1,0,1
  bit 6: 1,0,0 -> 0,1,1
  bit 7: 1,1,0 -> 1,1,0
Deduce rule: xor 0xAA.
Apply to 10100101:
  result = 00001111
Final: \boxed{00001111}


### Task: gravity
### Problem:
A mass of 49 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 = 49 * 981.
Step-by-step multiplication:
  4 * 10^1 * 981 = 39240
  running total = 39240
  9 * 10^0 * 981 = 8829
  running total = 48069
So F = 48069 centiNewtons = 480.69 N.
Final: \boxed{480.69}


### Task: numeral
### Problem:
Convert the Roman numeral II to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  I = 1  ->  0 + 1 = 1
  I = 1  ->  1 + 1 = 2
Final: \boxed{2}


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


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00010011 -> 00110001
  11011001 -> 10011101
  11100000 -> 00001110
Apply to: 11100001
### Reasoning:
<|cot_start|>Given examples:
  00010011 -> 00110001
  11011001 -> 10011101
  11100000 -> 00001110
Compare each bit position across the three examples:
  bit 0: 0,1,1 -> 0,1,0
  bit 1: 0,1,1 -> 0,0,0
  bit 2: 0,0,1 -> 1,0,0
  bit 3: 1,1,0 -> 1,1,0
  bit 4: 0,1,0 -> 0,1,1
  bit 5: 0,0,0 -> 0,1,1
  bit 6: 1,0,0 -> 0,0,1
  bit 7: 1,1,0 -> 1,1,0
Deduce rule: swap nibbles.
Apply to 11100001:
  result = 00011110
Final: \boxed{00011110}


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


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  98,40 -> 4098
  19,71 -> 7119
  34,55 -> 5534
Apply to: 64,44
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  98,40: '+' gives 138; target=4098  no
  98,40: '-' gives 58; target=4098  no
  98,40: '*' gives 3920; target=4098  no
  98,40: 'concat' gives 9840; target=4098  no
  98,40: 'rev_concat' gives 4098; target=4098  MATCH
  98,40: 'max*min+sum' gives 4058; target=4098  no
  98,40: 'digitsum2' gives 441; target=4098  no
  19,71: '+' gives 90; target=7119  no
  19,71: '-' gives 52; target=7119  no
  19,71: '*' gives 1349; target=7119  no
  19,71: 'concat' gives 1971; target=7119  no
  19,71: 'rev_concat' gives 7119; target=7119  MATCH
  19,71: 'max*min+sum' gives 1439; target=7119  no
  19,71: 'digitsum2' gives 324; target=7119  no
  34,55: '+' gives 89; target=5534  no
  34,55: '-' gives 21; target=5534  no
  34,55: '*' gives 1870; target=5534  no
  34,55: 'concat' gives 3455; target=5534  no
  34,55: 'rev_concat' gives 5534; target=5534  MATCH
  34,55: 'max*min+sum' gives 1959; target=5534  no
  34,55: 'digitsum2' gives 289; target=5534  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (64, 44):
  result = 4464
Final: \boxed{4464}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  57,46 -> 4657
  54,82 -> 8254
  12,40 -> 4012
Apply to: 85,11
### Reasoning:
<|cot_start|>Examples:
  57,46 -> 4657
  54,82 -> 8254
  12,40 -> 4012
Check both candidate forms:
  concat(57,46)=5746  rev_concat(57,46)=4657  target=4657  rev_concat
  concat(54,82)=5482  rev_concat(54,82)=8254  target=8254  rev_concat
  concat(12,40)=1240  rev_concat(12,40)=4012  target=4012  rev_concat
Conclude operator: rev_concat.
Apply to (85, 11):  answer = 1185
Final: \boxed{1185}


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


### Task: unit
### Problem:
Convert 70 kilometres to metres.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilometres = 1000 metres.
So 70 kilometres = 70 * 1000 metres.
Compute step by step:
  7 * 10^1 * 1000 = 70000
  running total = 70000
  0 * 10^0 * 1000 = 0
  running total = 70000
Final: \boxed{70000}


### Task: gravity
### Problem:
A mass of 23 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 = 23 * 981.
Step-by-step multiplication:
  2 * 10^1 * 981 = 19620
  running total = 19620
  3 * 10^0 * 981 = 2943
  running total = 22563
So F = 22563 centiNewtons = 225.63 N.
Final: \boxed{225.63}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01100111 -> 11110111
  11011000 -> 11111000
  10001011 -> 11111011
Apply to: 11010000
### Reasoning:
<|cot_start|>Given examples:
  01100111 -> 11110111
  11011000 -> 11111000
  10001011 -> 11111011
Compare each bit position across the three examples:
  bit 0: 0,1,1 -> 1,1,1
  bit 1: 1,1,0 -> 1,1,1
  bit 2: 1,0,0 -> 1,1,1
  bit 3: 0,1,0 -> 1,1,1
  bit 4: 0,1,1 -> 0,1,1
  bit 5: 1,0,0 -> 1,0,0
  bit 6: 1,0,1 -> 1,0,1
  bit 7: 1,0,1 -> 1,0,1
Deduce rule: or 0xF0.
Apply to 11010000:
  result = 11110000
Final: \boxed{11110000}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  81,35 -> 116
  83,96 -> 179
  95,10 -> 105
Apply to: 12,12
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  81,35: '+' gives 116; target=116  MATCH
  81,35: '-' gives 46; target=116  no
  81,35: '*' gives 2835; target=116  no
  81,35: 'concat' gives 8135; target=116  no
  81,35: 'rev_concat' gives 3581; target=116  no
  81,35: 'max*min+sum' gives 2951; target=116  no
  81,35: 'digitsum2' gives 289; target=116  no
  83,96: '+' gives 179; target=179  MATCH
  83,96: '-' gives 13; target=179  no
  83,96: '*' gives 7968; target=179  no
  83,96: 'concat' gives 8396; target=179  no
  83,96: 'rev_concat' gives 9683; target=179  no
  83,96: 'max*min+sum' gives 8147; target=179  no
  83,96: 'digitsum2' gives 676; target=179  no
  95,10: '+' gives 105; target=105  MATCH
  95,10: '-' gives 85; target=105  no
  95,10: '*' gives 950; target=105  no
  95,10: 'concat' gives 9510; target=105  no
  95,10: 'rev_concat' gives 1095; target=105  no
  95,10: 'max*min+sum' gives 1055; target=105  no
  95,10: 'digitsum2' gives 225; target=105  no
The only operator consistent with all examples is '+'.
Apply to (12, 12):
  result = 24
Final: \boxed{24}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  22,31 -> 64
  30,87 -> 324
  85,87 -> 784
Apply to: 16,66
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  22,31: '+' gives 53; target=64  no
  22,31: '-' gives 9; target=64  no
  22,31: '*' gives 682; target=64  no
  22,31: 'concat' gives 2231; target=64  no
  22,31: 'rev_concat' gives 3122; target=64  no
  22,31: 'max*min+sum' gives 735; target=64  no
  22,31: 'digitsum2' gives 64; target=64  MATCH
  30,87: '+' gives 117; target=324  no
  30,87: '-' gives 57; target=324  no
  30,87: '*' gives 2610; target=324  no
  30,87: 'concat' gives 3087; target=324  no
  30,87: 'rev_concat' gives 8730; target=324  no
  30,87: 'max*min+sum' gives 2727; target=324  no
  30,87: 'digitsum2' gives 324; target=324  MATCH
  85,87: '+' gives 172; target=784  no
  85,87: '-' gives 2; target=784  no
  85,87: '*' gives 7395; target=784  no
  85,87: 'concat' gives 8587; target=784  no
  85,87: 'rev_concat' gives 8785; target=784  no
  85,87: 'max*min+sum' gives 7567; target=784  no
  85,87: 'digitsum2' gives 784; target=784  MATCH
The only operator consistent with all examples is 'digitsum2'.
Apply to (16, 66):
  result = 361
Final: \boxed{361}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  39,24 -> 2439
  92,16 -> 1692
  58,66 -> 6658
Apply to: 58,92
### Reasoning:
<|cot_start|>Examples:
  39,24 -> 2439
  92,16 -> 1692
  58,66 -> 6658
Check both candidate forms:
  concat(39,24)=3924  rev_concat(39,24)=2439  target=2439  rev_concat
  concat(92,16)=9216  rev_concat(92,16)=1692  target=1692  rev_concat
  concat(58,66)=5866  rev_concat(58,66)=6658  target=6658  rev_concat
Conclude operator: rev_concat.
Apply to (58, 92):  answer = 9258
Final: \boxed{9258}


### Task: unit
### Problem:
Convert 89 minutes to seconds.
### Reasoning:
<|cot_start|>Conversion factor: 1 minutes = 60 seconds.
So 89 minutes = 89 * 60 seconds.
Compute step by step:
  8 * 10^1 * 60 = 4800
  running total = 4800
  9 * 10^0 * 60 = 540
  running total = 5340
Final: \boxed{5340}


### Task: numeral
### Problem:
Convert the Roman numeral LXX 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
Final: \boxed{70}


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