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


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  11,42 -> 4211
  64,77 -> 7764
  94,84 -> 8494
Apply to: 46,18
### Reasoning:
<|cot_start|>Examples:
  11,42 -> 4211
  64,77 -> 7764
  94,84 -> 8494
Check both candidate forms:
  concat(11,42)=1142  rev_concat(11,42)=4211  target=4211  rev_concat
  concat(64,77)=6477  rev_concat(64,77)=7764  target=7764  rev_concat
  concat(94,84)=9484  rev_concat(94,84)=8494  target=8494  rev_concat
Conclude operator: rev_concat.
Apply to (46, 18):  answer = 1846
Final: \boxed{1846}


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


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  84,53 -> 5384
  43,52 -> 5243
  39,16 -> 1639
Apply to: 76,40
### Reasoning:
<|cot_start|>Examples:
  84,53 -> 5384
  43,52 -> 5243
  39,16 -> 1639
Check both candidate forms:
  concat(84,53)=8453  rev_concat(84,53)=5384  target=5384  rev_concat
  concat(43,52)=4352  rev_concat(43,52)=5243  target=5243  rev_concat
  concat(39,16)=3916  rev_concat(39,16)=1639  target=1639  rev_concat
Conclude operator: rev_concat.
Apply to (76, 40):  answer = 4076
Final: \boxed{4076}


### 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: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  31,53 -> 3153
  63,37 -> 6337
  78,42 -> 7842
Apply to: 55,90
### Reasoning:
<|cot_start|>Examples:
  31,53 -> 3153
  63,37 -> 6337
  78,42 -> 7842
Check both candidate forms:
  concat(31,53)=3153  rev_concat(31,53)=5331  target=3153  concat
  concat(63,37)=6337  rev_concat(63,37)=3763  target=6337  concat
  concat(78,42)=7842  rev_concat(78,42)=4278  target=7842  concat
Conclude operator: concat.
Apply to (55, 90):  answer = 5590
Final: \boxed{5590}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  56,47 -> 2632
  67,53 -> 3551
  41,30 -> 1230
Apply to: 69,26
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  56,47: '+' gives 103; target=2632  no
  56,47: '-' gives 9; target=2632  no
  56,47: '*' gives 2632; target=2632  MATCH
  56,47: 'concat' gives 5647; target=2632  no
  56,47: 'rev_concat' gives 4756; target=2632  no
  56,47: 'max*min+sum' gives 2735; target=2632  no
  56,47: 'digitsum2' gives 484; target=2632  no
  67,53: '+' gives 120; target=3551  no
  67,53: '-' gives 14; target=3551  no
  67,53: '*' gives 3551; target=3551  MATCH
  67,53: 'concat' gives 6753; target=3551  no
  67,53: 'rev_concat' gives 5367; target=3551  no
  67,53: 'max*min+sum' gives 3671; target=3551  no
  67,53: 'digitsum2' gives 441; target=3551  no
  41,30: '+' gives 71; target=1230  no
  41,30: '-' gives 11; target=1230  no
  41,30: '*' gives 1230; target=1230  MATCH
  41,30: 'concat' gives 4130; target=1230  no
  41,30: 'rev_concat' gives 3041; target=1230  no
  41,30: 'max*min+sum' gives 1301; target=1230  no
  41,30: 'digitsum2' gives 64; target=1230  no
The only operator consistent with all examples is '*'.
Apply to (69, 26):
  result = 1794
Final: \boxed{1794}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  77,44 -> 7744
  43,11 -> 4311
  59,60 -> 5960
Apply to: 35,13
### Reasoning:
<|cot_start|>Examples:
  77,44 -> 7744
  43,11 -> 4311
  59,60 -> 5960
Check both candidate forms:
  concat(77,44)=7744  rev_concat(77,44)=4477  target=7744  concat
  concat(43,11)=4311  rev_concat(43,11)=1143  target=4311  concat
  concat(59,60)=5960  rev_concat(59,60)=6059  target=5960  concat
Conclude operator: concat.
Apply to (35, 13):  answer = 3513
Final: \boxed{3513}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  84,91 -> 175
  26,50 -> 76
  45,47 -> 92
Apply to: 67,53
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  84,91: '+' gives 175; target=175  MATCH
  84,91: '-' gives 7; target=175  no
  84,91: '*' gives 7644; target=175  no
  84,91: 'concat' gives 8491; target=175  no
  84,91: 'rev_concat' gives 9184; target=175  no
  84,91: 'max*min+sum' gives 7819; target=175  no
  84,91: 'digitsum2' gives 484; target=175  no
  26,50: '+' gives 76; target=76  MATCH
  26,50: '-' gives 24; target=76  no
  26,50: '*' gives 1300; target=76  no
  26,50: 'concat' gives 2650; target=76  no
  26,50: 'rev_concat' gives 5026; target=76  no
  26,50: 'max*min+sum' gives 1376; target=76  no
  26,50: 'digitsum2' gives 169; target=76  no
  45,47: '+' gives 92; target=92  MATCH
  45,47: '-' gives 2; target=92  no
  45,47: '*' gives 2115; target=92  no
  45,47: 'concat' gives 4547; target=92  no
  45,47: 'rev_concat' gives 4745; target=92  no
  45,47: 'max*min+sum' gives 2207; target=92  no
  45,47: 'digitsum2' gives 400; target=92  no
The only operator consistent with all examples is '+'.
Apply to (67, 53):
  result = 120
Final: \boxed{120}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  47,35 -> 3547
  93,56 -> 5693
  41,82 -> 8241
Apply to: 20,38
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  47,35: '+' gives 82; target=3547  no
  47,35: '-' gives 12; target=3547  no
  47,35: '*' gives 1645; target=3547  no
  47,35: 'concat' gives 4735; target=3547  no
  47,35: 'rev_concat' gives 3547; target=3547  MATCH
  47,35: 'max*min+sum' gives 1727; target=3547  no
  47,35: 'digitsum2' gives 361; target=3547  no
  93,56: '+' gives 149; target=5693  no
  93,56: '-' gives 37; target=5693  no
  93,56: '*' gives 5208; target=5693  no
  93,56: 'concat' gives 9356; target=5693  no
  93,56: 'rev_concat' gives 5693; target=5693  MATCH
  93,56: 'max*min+sum' gives 5357; target=5693  no
  93,56: 'digitsum2' gives 529; target=5693  no
  41,82: '+' gives 123; target=8241  no
  41,82: '-' gives 41; target=8241  no
  41,82: '*' gives 3362; target=8241  no
  41,82: 'concat' gives 4182; target=8241  no
  41,82: 'rev_concat' gives 8241; target=8241  MATCH
  41,82: 'max*min+sum' gives 3485; target=8241  no
  41,82: 'digitsum2' gives 225; target=8241  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (20, 38):
  result = 3820
Final: \boxed{3820}


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


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  32,28 -> 896
  25,46 -> 1150
  47,32 -> 1504
Apply to: 72,47
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  32,28: '+' gives 60; target=896  no
  32,28: '-' gives 4; target=896  no
  32,28: '*' gives 896; target=896  MATCH
  32,28: 'concat' gives 3228; target=896  no
  32,28: 'rev_concat' gives 2832; target=896  no
  32,28: 'max*min+sum' gives 956; target=896  no
  32,28: 'digitsum2' gives 225; target=896  no
  25,46: '+' gives 71; target=1150  no
  25,46: '-' gives 21; target=1150  no
  25,46: '*' gives 1150; target=1150  MATCH
  25,46: 'concat' gives 2546; target=1150  no
  25,46: 'rev_concat' gives 4625; target=1150  no
  25,46: 'max*min+sum' gives 1221; target=1150  no
  25,46: 'digitsum2' gives 289; target=1150  no
  47,32: '+' gives 79; target=1504  no
  47,32: '-' gives 15; target=1504  no
  47,32: '*' gives 1504; target=1504  MATCH
  47,32: 'concat' gives 4732; target=1504  no
  47,32: 'rev_concat' gives 3247; target=1504  no
  47,32: 'max*min+sum' gives 1583; target=1504  no
  47,32: 'digitsum2' gives 256; target=1504  no
The only operator consistent with all examples is '*'.
Apply to (72, 47):
  result = 3384
Final: \boxed{3384}


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


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  42,75 -> 4275
  39,73 -> 3973
  84,37 -> 8437
Apply to: 82,16
### Reasoning:
<|cot_start|>Examples:
  42,75 -> 4275
  39,73 -> 3973
  84,37 -> 8437
Check both candidate forms:
  concat(42,75)=4275  rev_concat(42,75)=7542  target=4275  concat
  concat(39,73)=3973  rev_concat(39,73)=7339  target=3973  concat
  concat(84,37)=8437  rev_concat(84,37)=3784  target=8437  concat
Conclude operator: concat.
Apply to (82, 16):  answer = 8216
Final: \boxed{8216}


### Task: unit
### Problem:
Convert 62 kilometres to metres.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilometres = 1000 metres.
So 62 kilometres = 62 * 1000 metres.
Compute step by step:
  6 * 10^1 * 1000 = 60000
  running total = 60000
  2 * 10^0 * 1000 = 2000
  running total = 62000
Final: \boxed{62000}


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


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  54,49 -> 5449
  28,47 -> 2847
  73,43 -> 7343
Apply to: 60,86
### Reasoning:
<|cot_start|>Examples:
  54,49 -> 5449
  28,47 -> 2847
  73,43 -> 7343
Check both candidate forms:
  concat(54,49)=5449  rev_concat(54,49)=4954  target=5449  concat
  concat(28,47)=2847  rev_concat(28,47)=4728  target=2847  concat
  concat(73,43)=7343  rev_concat(73,43)=4373  target=7343  concat
Conclude operator: concat.
Apply to (60, 86):  answer = 6086
Final: \boxed{6086}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00110100 -> 11001011
  11101011 -> 00010100
  01011101 -> 10100010
Apply to: 01100101
### Reasoning:
<|cot_start|>Given examples:
  00110100 -> 11001011
  11101011 -> 00010100
  01011101 -> 10100010
Compare each bit position across the three examples:
  bit 0: 0,1,0 -> 1,0,1
  bit 1: 0,1,1 -> 1,0,0
  bit 2: 1,1,0 -> 0,0,1
  bit 3: 1,0,1 -> 0,1,0
  bit 4: 0,1,1 -> 1,0,0
  bit 5: 1,0,1 -> 0,1,0
  bit 6: 0,1,0 -> 1,0,1
  bit 7: 0,1,1 -> 1,0,0
Deduce rule: invert (NOT).
Apply to 01100101:
  result = 10011010
Final: \boxed{10011010}


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


### Task: numeral
### Problem:
Convert the Roman numeral LII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  I = 1  ->  50 + 1 = 51
  I = 1  ->  51 + 1 = 52
Final: \boxed{52}


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


### Task: numeral
### Problem:
Convert the Roman numeral LXXIX to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  X = 10  ->  50 + 10 = 60
  X = 10  ->  60 + 10 = 70
  IX = 9  ->  70 + 9 = 79
Final: \boxed{79}


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


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  48,52 -> 361
  48,87 -> 729
  29,72 -> 400
Apply to: 66,10
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  48,52: '+' gives 100; target=361  no
  48,52: '-' gives 4; target=361  no
  48,52: '*' gives 2496; target=361  no
  48,52: 'concat' gives 4852; target=361  no
  48,52: 'rev_concat' gives 5248; target=361  no
  48,52: 'max*min+sum' gives 2596; target=361  no
  48,52: 'digitsum2' gives 361; target=361  MATCH
  48,87: '+' gives 135; target=729  no
  48,87: '-' gives 39; target=729  no
  48,87: '*' gives 4176; target=729  no
  48,87: 'concat' gives 4887; target=729  no
  48,87: 'rev_concat' gives 8748; target=729  no
  48,87: 'max*min+sum' gives 4311; target=729  no
  48,87: 'digitsum2' gives 729; target=729  MATCH
  29,72: '+' gives 101; target=400  no
  29,72: '-' gives 43; target=400  no
  29,72: '*' gives 2088; target=400  no
  29,72: 'concat' gives 2972; target=400  no
  29,72: 'rev_concat' gives 7229; target=400  no
  29,72: 'max*min+sum' gives 2189; target=400  no
  29,72: 'digitsum2' gives 400; target=400  MATCH
The only operator consistent with all examples is 'digitsum2'.
Apply to (66, 10):
  result = 169
Final: \boxed{169}


### Task: gravity
### Problem:
A mass of 36 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 36 * 981.
Step-by-step multiplication:
  3 * 10^1 * 981 = 29430
  running total = 29430
  6 * 10^0 * 981 = 5886
  running total = 35316
So F = 35316 centiNewtons = 353.16 N.
Final: \boxed{353.16}


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


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10111100 -> 00001100
  01011111 -> 00001111
  11011001 -> 00001001
Apply to: 00000100
### Reasoning:
<|cot_start|>Given examples:
  10111100 -> 00001100
  01011111 -> 00001111
  11011001 -> 00001001
Compare each bit position across the three examples:
  bit 0: 1,0,1 -> 0,0,0
  bit 1: 0,1,1 -> 0,0,0
  bit 2: 1,0,0 -> 0,0,0
  bit 3: 1,1,1 -> 0,0,0
  bit 4: 1,1,1 -> 1,1,1
  bit 5: 1,1,0 -> 1,1,0
  bit 6: 0,1,0 -> 0,1,0
  bit 7: 0,1,1 -> 0,1,1
Deduce rule: and 0x0F.
Apply to 00000100:
  result = 00000100
Final: \boxed{00000100}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  60,18 -> 6018
  84,70 -> 8470
  66,96 -> 6696
Apply to: 22,31
### Reasoning:
<|cot_start|>Examples:
  60,18 -> 6018
  84,70 -> 8470
  66,96 -> 6696
Check both candidate forms:
  concat(60,18)=6018  rev_concat(60,18)=1860  target=6018  concat
  concat(84,70)=8470  rev_concat(84,70)=7084  target=8470  concat
  concat(66,96)=6696  rev_concat(66,96)=9666  target=6696  concat
Conclude operator: concat.
Apply to (22, 31):  answer = 2231
Final: \boxed{2231}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00000000 -> 00000000
  11011110 -> 01111011
  10010011 -> 11001001
Apply to: 11111000
### Reasoning:
<|cot_start|>Given examples:
  00000000 -> 00000000
  11011110 -> 01111011
  10010011 -> 11001001
Compare each bit position across the three examples:
  bit 0: 0,1,1 -> 0,0,1
  bit 1: 0,1,0 -> 0,1,1
  bit 2: 0,0,0 -> 0,1,0
  bit 3: 0,1,1 -> 0,1,0
  bit 4: 0,1,0 -> 0,1,1
  bit 5: 0,1,0 -> 0,0,0
  bit 6: 0,1,1 -> 0,1,0
  bit 7: 0,0,1 -> 0,1,1
Deduce rule: reverse bits.
Apply to 11111000:
  result = 00011111
Final: \boxed{00011111}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11010111 -> 10000010
  00011101 -> 01001000
  10010111 -> 11000010
Apply to: 01010111
### Reasoning:
<|cot_start|>Given examples:
  11010111 -> 10000010
  00011101 -> 01001000
  10010111 -> 11000010
Compare each bit position across the three examples:
  bit 0: 1,0,1 -> 1,0,1
  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: 0,1,0 -> 0,1,0
  bit 5: 1,1,1 -> 0,0,0
  bit 6: 1,0,1 -> 1,0,1
  bit 7: 1,1,1 -> 0,0,0
Deduce rule: xor 0x55.
Apply to 01010111:
  result = 00000010
Final: \boxed{00000010}


### Task: numeral
### Problem:
Convert the Roman numeral LXIII 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
  I = 1  ->  62 + 1 = 63
Final: \boxed{63}


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


### 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: equation
### Problem:
Discover the operator from examples then apply it:
  46,20 -> 66
  83,84 -> 167
  22,37 -> 59
Apply to: 48,61
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  46,20: '+' gives 66; target=66  MATCH
  46,20: '-' gives 26; target=66  no
  46,20: '*' gives 920; target=66  no
  46,20: 'concat' gives 4620; target=66  no
  46,20: 'rev_concat' gives 2046; target=66  no
  46,20: 'max*min+sum' gives 986; target=66  no
  46,20: 'digitsum2' gives 144; target=66  no
  83,84: '+' gives 167; target=167  MATCH
  83,84: '-' gives 1; target=167  no
  83,84: '*' gives 6972; target=167  no
  83,84: 'concat' gives 8384; target=167  no
  83,84: 'rev_concat' gives 8483; target=167  no
  83,84: 'max*min+sum' gives 7139; target=167  no
  83,84: 'digitsum2' gives 529; target=167  no
  22,37: '+' gives 59; target=59  MATCH
  22,37: '-' gives 15; target=59  no
  22,37: '*' gives 814; target=59  no
  22,37: 'concat' gives 2237; target=59  no
  22,37: 'rev_concat' gives 3722; target=59  no
  22,37: 'max*min+sum' gives 873; target=59  no
  22,37: 'digitsum2' gives 196; target=59  no
The only operator consistent with all examples is '+'.
Apply to (48, 61):
  result = 109
Final: \boxed{109}


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


### Task: gravity
### Problem:
A mass of 5 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 = 5 * 981.
Step-by-step multiplication:
  5 * 10^0 * 981 = 4905
  running total = 4905
So F = 4905 centiNewtons = 49.05 N.
Final: \boxed{49.05}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  25,89 -> 2589
  98,11 -> 9811
  90,77 -> 9077
Apply to: 90,22
### Reasoning:
<|cot_start|>Examples:
  25,89 -> 2589
  98,11 -> 9811
  90,77 -> 9077
Check both candidate forms:
  concat(25,89)=2589  rev_concat(25,89)=8925  target=2589  concat
  concat(98,11)=9811  rev_concat(98,11)=1198  target=9811  concat
  concat(90,77)=9077  rev_concat(90,77)=7790  target=9077  concat
Conclude operator: concat.
Apply to (90, 22):  answer = 9022
Final: \boxed{9022}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  89,48 -> 4889
  67,52 -> 5267
  92,13 -> 1392
Apply to: 81,58
### Reasoning:
<|cot_start|>Examples:
  89,48 -> 4889
  67,52 -> 5267
  92,13 -> 1392
Check both candidate forms:
  concat(89,48)=8948  rev_concat(89,48)=4889  target=4889  rev_concat
  concat(67,52)=6752  rev_concat(67,52)=5267  target=5267  rev_concat
  concat(92,13)=9213  rev_concat(92,13)=1392  target=1392  rev_concat
Conclude operator: rev_concat.
Apply to (81, 58):  answer = 5881
Final: \boxed{5881}


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


### Task: unit
### Problem:
Convert 66 minutes to seconds.
### Reasoning:
<|cot_start|>Conversion factor: 1 minutes = 60 seconds.
So 66 minutes = 66 * 60 seconds.
Compute step by step:
  6 * 10^1 * 60 = 3600
  running total = 3600
  6 * 10^0 * 60 = 360
  running total = 3960
Final: \boxed{3960}


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


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  75,90 -> 7590
  16,35 -> 1635
  53,68 -> 5368
Apply to: 33,82
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  75,90: '+' gives 165; target=7590  no
  75,90: '-' gives 15; target=7590  no
  75,90: '*' gives 6750; target=7590  no
  75,90: 'concat' gives 7590; target=7590  MATCH
  75,90: 'rev_concat' gives 9075; target=7590  no
  75,90: 'max*min+sum' gives 6915; target=7590  no
  75,90: 'digitsum2' gives 441; target=7590  no
  16,35: '+' gives 51; target=1635  no
  16,35: '-' gives 19; target=1635  no
  16,35: '*' gives 560; target=1635  no
  16,35: 'concat' gives 1635; target=1635  MATCH
  16,35: 'rev_concat' gives 3516; target=1635  no
  16,35: 'max*min+sum' gives 611; target=1635  no
  16,35: 'digitsum2' gives 225; target=1635  no
  53,68: '+' gives 121; target=5368  no
  53,68: '-' gives 15; target=5368  no
  53,68: '*' gives 3604; target=5368  no
  53,68: 'concat' gives 5368; target=5368  MATCH
  53,68: 'rev_concat' gives 6853; target=5368  no
  53,68: 'max*min+sum' gives 3725; target=5368  no
  53,68: 'digitsum2' gives 484; target=5368  no
The only operator consistent with all examples is 'concat'.
Apply to (33, 82):
  result = 3382
Final: \boxed{3382}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  30,50 -> 3050
  37,63 -> 3763
  69,41 -> 6941
Apply to: 45,76
### Reasoning:
<|cot_start|>Examples:
  30,50 -> 3050
  37,63 -> 3763
  69,41 -> 6941
Check both candidate forms:
  concat(30,50)=3050  rev_concat(30,50)=5030  target=3050  concat
  concat(37,63)=3763  rev_concat(37,63)=6337  target=3763  concat
  concat(69,41)=6941  rev_concat(69,41)=4169  target=6941  concat
Conclude operator: concat.
Apply to (45, 76):  answer = 4576
Final: \boxed{4576}


### Task: unit
### Problem:
Convert 13 minutes to seconds.
### Reasoning:
<|cot_start|>Conversion factor: 1 minutes = 60 seconds.
So 13 minutes = 13 * 60 seconds.
Compute step by step:
  1 * 10^1 * 60 = 600
  running total = 600
  3 * 10^0 * 60 = 180
  running total = 780
Final: \boxed{780}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11010011 -> 00000011
  11001000 -> 00001000
  01010010 -> 00000010
Apply to: 01001110
### Reasoning:
<|cot_start|>Given examples:
  11010011 -> 00000011
  11001000 -> 00001000
  01010010 -> 00000010
Compare each bit position across the three examples:
  bit 0: 1,1,0 -> 0,0,0
  bit 1: 1,1,1 -> 0,0,0
  bit 2: 0,0,0 -> 0,0,0
  bit 3: 1,0,1 -> 0,0,0
  bit 4: 0,1,0 -> 0,1,0
  bit 5: 0,0,0 -> 0,0,0
  bit 6: 1,0,1 -> 1,0,1
  bit 7: 1,0,0 -> 1,0,0
Deduce rule: and 0x0F.
Apply to 01001110:
  result = 00001110
Final: \boxed{00001110}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  13,15 -> 28
  60,61 -> 121
  46,31 -> 77
Apply to: 58,13
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  13,15: '+' gives 28; target=28  MATCH
  13,15: '-' gives 2; target=28  no
  13,15: '*' gives 195; target=28  no
  13,15: 'concat' gives 1315; target=28  no
  13,15: 'rev_concat' gives 1513; target=28  no
  13,15: 'max*min+sum' gives 223; target=28  no
  13,15: 'digitsum2' gives 100; target=28  no
  60,61: '+' gives 121; target=121  MATCH
  60,61: '-' gives 1; target=121  no
  60,61: '*' gives 3660; target=121  no
  60,61: 'concat' gives 6061; target=121  no
  60,61: 'rev_concat' gives 6160; target=121  no
  60,61: 'max*min+sum' gives 3781; target=121  no
  60,61: 'digitsum2' gives 169; target=121  no
  46,31: '+' gives 77; target=77  MATCH
  46,31: '-' gives 15; target=77  no
  46,31: '*' gives 1426; target=77  no
  46,31: 'concat' gives 4631; target=77  no
  46,31: 'rev_concat' gives 3146; target=77  no
  46,31: 'max*min+sum' gives 1503; target=77  no
  46,31: 'digitsum2' gives 196; target=77  no
The only operator consistent with all examples is '+'.
Apply to (58, 13):
  result = 71
Final: \boxed{71}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11011101 -> 00001101
  00101001 -> 00001001
  00111010 -> 00001010
Apply to: 11110010
### Reasoning:
<|cot_start|>Given examples:
  11011101 -> 00001101
  00101001 -> 00001001
  00111010 -> 00001010
Compare each bit position across the three examples:
  bit 0: 1,0,0 -> 0,0,0
  bit 1: 1,0,0 -> 0,0,0
  bit 2: 0,1,1 -> 0,0,0
  bit 3: 1,0,1 -> 0,0,0
  bit 4: 1,1,1 -> 1,1,1
  bit 5: 1,0,0 -> 1,0,0
  bit 6: 0,0,1 -> 0,0,1
  bit 7: 1,1,0 -> 1,1,0
Deduce rule: and 0x0F.
Apply to 11110010:
  result = 00000010
Final: \boxed{00000010}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  31,55 -> 5531
  42,69 -> 6942
  43,67 -> 6743
Apply to: 33,60
### Reasoning:
<|cot_start|>Examples:
  31,55 -> 5531
  42,69 -> 6942
  43,67 -> 6743
Check both candidate forms:
  concat(31,55)=3155  rev_concat(31,55)=5531  target=5531  rev_concat
  concat(42,69)=4269  rev_concat(42,69)=6942  target=6942  rev_concat
  concat(43,67)=4367  rev_concat(43,67)=6743  target=6743  rev_concat
Conclude operator: rev_concat.
Apply to (33, 60):  answer = 6033
Final: \boxed{6033}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  49,26 -> 4926
  30,54 -> 3054
  36,83 -> 3683
Apply to: 85,30
### Reasoning:
<|cot_start|>Examples:
  49,26 -> 4926
  30,54 -> 3054
  36,83 -> 3683
Check both candidate forms:
  concat(49,26)=4926  rev_concat(49,26)=2649  target=4926  concat
  concat(30,54)=3054  rev_concat(30,54)=5430  target=3054  concat
  concat(36,83)=3683  rev_concat(36,83)=8336  target=3683  concat
Conclude operator: concat.
Apply to (85, 30):  answer = 8530
Final: \boxed{8530}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  37,30 -> 3730
  67,11 -> 6711
  30,10 -> 3010
Apply to: 31,83
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  37,30: '+' gives 67; target=3730  no
  37,30: '-' gives 7; target=3730  no
  37,30: '*' gives 1110; target=3730  no
  37,30: 'concat' gives 3730; target=3730  MATCH
  37,30: 'rev_concat' gives 3037; target=3730  no
  37,30: 'max*min+sum' gives 1177; target=3730  no
  37,30: 'digitsum2' gives 169; target=3730  no
  67,11: '+' gives 78; target=6711  no
  67,11: '-' gives 56; target=6711  no
  67,11: '*' gives 737; target=6711  no
  67,11: 'concat' gives 6711; target=6711  MATCH
  67,11: 'rev_concat' gives 1167; target=6711  no
  67,11: 'max*min+sum' gives 815; target=6711  no
  67,11: 'digitsum2' gives 225; target=6711  no
  30,10: '+' gives 40; target=3010  no
  30,10: '-' gives 20; target=3010  no
  30,10: '*' gives 300; target=3010  no
  30,10: 'concat' gives 3010; target=3010  MATCH
  30,10: 'rev_concat' gives 1030; target=3010  no
  30,10: 'max*min+sum' gives 340; target=3010  no
  30,10: 'digitsum2' gives 16; target=3010  no
The only operator consistent with all examples is 'concat'.
Apply to (31, 83):
  result = 3183
Final: \boxed{3183}


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


### Task: unit
### Problem:
Convert 76 hours to minutes.
### Reasoning:
<|cot_start|>Conversion factor: 1 hours = 60 minutes.
So 76 hours = 76 * 60 minutes.
Compute step by step:
  7 * 10^1 * 60 = 4200
  running total = 4200
  6 * 10^0 * 60 = 360
  running total = 4560
Final: \boxed{4560}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  89,31 -> 2879
  61,13 -> 867
  95,19 -> 1919
Apply to: 33,59
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  89,31: '+' gives 120; target=2879  no
  89,31: '-' gives 58; target=2879  no
  89,31: '*' gives 2759; target=2879  no
  89,31: 'concat' gives 8931; target=2879  no
  89,31: 'rev_concat' gives 3189; target=2879  no
  89,31: 'max*min+sum' gives 2879; target=2879  MATCH
  89,31: 'digitsum2' gives 441; target=2879  no
  61,13: '+' gives 74; target=867  no
  61,13: '-' gives 48; target=867  no
  61,13: '*' gives 793; target=867  no
  61,13: 'concat' gives 6113; target=867  no
  61,13: 'rev_concat' gives 1361; target=867  no
  61,13: 'max*min+sum' gives 867; target=867  MATCH
  61,13: 'digitsum2' gives 121; target=867  no
  95,19: '+' gives 114; target=1919  no
  95,19: '-' gives 76; target=1919  no
  95,19: '*' gives 1805; target=1919  no
  95,19: 'concat' gives 9519; target=1919  no
  95,19: 'rev_concat' gives 1995; target=1919  no
  95,19: 'max*min+sum' gives 1919; target=1919  MATCH
  95,19: 'digitsum2' gives 576; target=1919  no
The only operator consistent with all examples is 'max*min+sum'.
Apply to (33, 59):
  result = 2039
Final: \boxed{2039}


### Task: gravity
### Problem:
A mass of 47 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 = 47 * 981.
Step-by-step multiplication:
  4 * 10^1 * 981 = 39240
  running total = 39240
  7 * 10^0 * 981 = 6867
  running total = 46107
So F = 46107 centiNewtons = 461.07 N.
Final: \boxed{461.07}


### 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: equation
### Problem:
Discover the operator from examples then apply it:
  63,76 -> 4927
  35,75 -> 2735
  55,86 -> 4871
Apply to: 41,96
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  63,76: '+' gives 139; target=4927  no
  63,76: '-' gives 13; target=4927  no
  63,76: '*' gives 4788; target=4927  no
  63,76: 'concat' gives 6376; target=4927  no
  63,76: 'rev_concat' gives 7663; target=4927  no
  63,76: 'max*min+sum' gives 4927; target=4927  MATCH
  63,76: 'digitsum2' gives 484; target=4927  no
  35,75: '+' gives 110; target=2735  no
  35,75: '-' gives 40; target=2735  no
  35,75: '*' gives 2625; target=2735  no
  35,75: 'concat' gives 3575; target=2735  no
  35,75: 'rev_concat' gives 7535; target=2735  no
  35,75: 'max*min+sum' gives 2735; target=2735  MATCH
  35,75: 'digitsum2' gives 400; target=2735  no
  55,86: '+' gives 141; target=4871  no
  55,86: '-' gives 31; target=4871  no
  55,86: '*' gives 4730; target=4871  no
  55,86: 'concat' gives 5586; target=4871  no
  55,86: 'rev_concat' gives 8655; target=4871  no
  55,86: 'max*min+sum' gives 4871; target=4871  MATCH
  55,86: 'digitsum2' gives 576; target=4871  no
The only operator consistent with all examples is 'max*min+sum'.
Apply to (41, 96):
  result = 4073
Final: \boxed{4073}


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


### 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: equation
### Problem:
Discover the operator from examples then apply it:
  32,56 -> 1880
  59,93 -> 5639
  77,89 -> 7019
Apply to: 96,57
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  32,56: '+' gives 88; target=1880  no
  32,56: '-' gives 24; target=1880  no
  32,56: '*' gives 1792; target=1880  no
  32,56: 'concat' gives 3256; target=1880  no
  32,56: 'rev_concat' gives 5632; target=1880  no
  32,56: 'max*min+sum' gives 1880; target=1880  MATCH
  32,56: 'digitsum2' gives 256; target=1880  no
  59,93: '+' gives 152; target=5639  no
  59,93: '-' gives 34; target=5639  no
  59,93: '*' gives 5487; target=5639  no
  59,93: 'concat' gives 5993; target=5639  no
  59,93: 'rev_concat' gives 9359; target=5639  no
  59,93: 'max*min+sum' gives 5639; target=5639  MATCH
  59,93: 'digitsum2' gives 676; target=5639  no
  77,89: '+' gives 166; target=7019  no
  77,89: '-' gives 12; target=7019  no
  77,89: '*' gives 6853; target=7019  no
  77,89: 'concat' gives 7789; target=7019  no
  77,89: 'rev_concat' gives 8977; target=7019  no
  77,89: 'max*min+sum' gives 7019; target=7019  MATCH
  77,89: 'digitsum2' gives 961; target=7019  no
The only operator consistent with all examples is 'max*min+sum'.
Apply to (96, 57):
  result = 5625
Final: \boxed{5625}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  38,86 -> 8638
  82,66 -> 6682
  87,46 -> 4687
Apply to: 22,27
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  38,86: '+' gives 124; target=8638  no
  38,86: '-' gives 48; target=8638  no
  38,86: '*' gives 3268; target=8638  no
  38,86: 'concat' gives 3886; target=8638  no
  38,86: 'rev_concat' gives 8638; target=8638  MATCH
  38,86: 'max*min+sum' gives 3392; target=8638  no
  38,86: 'digitsum2' gives 625; target=8638  no
  82,66: '+' gives 148; target=6682  no
  82,66: '-' gives 16; target=6682  no
  82,66: '*' gives 5412; target=6682  no
  82,66: 'concat' gives 8266; target=6682  no
  82,66: 'rev_concat' gives 6682; target=6682  MATCH
  82,66: 'max*min+sum' gives 5560; target=6682  no
  82,66: 'digitsum2' gives 484; target=6682  no
  87,46: '+' gives 133; target=4687  no
  87,46: '-' gives 41; target=4687  no
  87,46: '*' gives 4002; target=4687  no
  87,46: 'concat' gives 8746; target=4687  no
  87,46: 'rev_concat' gives 4687; target=4687  MATCH
  87,46: 'max*min+sum' gives 4135; target=4687  no
  87,46: 'digitsum2' gives 625; target=4687  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (22, 27):
  result = 2722
Final: \boxed{2722}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00001111 -> 11110000
  11111100 -> 00000011
  11000111 -> 00111000
Apply to: 10110011
### Reasoning:
<|cot_start|>Given examples:
  00001111 -> 11110000
  11111100 -> 00000011
  11000111 -> 00111000
Compare each bit position across the three examples:
  bit 0: 0,1,1 -> 1,0,0
  bit 1: 0,1,1 -> 1,0,0
  bit 2: 0,1,0 -> 1,0,1
  bit 3: 0,1,0 -> 1,0,1
  bit 4: 1,1,0 -> 0,0,1
  bit 5: 1,1,1 -> 0,0,0
  bit 6: 1,0,1 -> 0,1,0
  bit 7: 1,0,1 -> 0,1,0
Deduce rule: invert (NOT).
Apply to 10110011:
  result = 01001100
Final: \boxed{01001100}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01010001 -> 00000100
  00000001 -> 01010100
  10011010 -> 11001111
Apply to: 01011110
### Reasoning:
<|cot_start|>Given examples:
  01010001 -> 00000100
  00000001 -> 01010100
  10011010 -> 11001111
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 0,0,1
  bit 1: 1,0,0 -> 0,1,1
  bit 2: 0,0,0 -> 0,0,0
  bit 3: 1,0,1 -> 0,1,0
  bit 4: 0,0,1 -> 0,0,1
  bit 5: 0,0,0 -> 1,1,1
  bit 6: 0,0,1 -> 0,0,1
  bit 7: 1,1,0 -> 0,0,1
Deduce rule: xor 0x55.
Apply to 01011110:
  result = 00001011
Final: \boxed{00001011}


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