### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  14,51 -> 1451
  13,96 -> 1396
  11,68 -> 1168
Apply to: 42,37
### Reasoning:
<|cot_start|>Examples:
  14,51 -> 1451
  13,96 -> 1396
  11,68 -> 1168
Check both candidate forms:
  concat(14,51)=1451  rev_concat(14,51)=5114  target=1451  concat
  concat(13,96)=1396  rev_concat(13,96)=9613  target=1396  concat
  concat(11,68)=1168  rev_concat(11,68)=6811  target=1168  concat
Conclude operator: concat.
Apply to (42, 37):  answer = 4237
Final: \boxed{4237}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  63,68 -> 6368
  19,22 -> 1922
  68,90 -> 6890
Apply to: 28,58
### Reasoning:
<|cot_start|>Examples:
  63,68 -> 6368
  19,22 -> 1922
  68,90 -> 6890
Check both candidate forms:
  concat(63,68)=6368  rev_concat(63,68)=6863  target=6368  concat
  concat(19,22)=1922  rev_concat(19,22)=2219  target=1922  concat
  concat(68,90)=6890  rev_concat(68,90)=9068  target=6890  concat
Conclude operator: concat.
Apply to (28, 58):  answer = 2858
Final: \boxed{2858}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  57,23 -> 5723
  62,43 -> 6243
  52,86 -> 5286
Apply to: 81,77
### Reasoning:
<|cot_start|>Examples:
  57,23 -> 5723
  62,43 -> 6243
  52,86 -> 5286
Check both candidate forms:
  concat(57,23)=5723  rev_concat(57,23)=2357  target=5723  concat
  concat(62,43)=6243  rev_concat(62,43)=4362  target=6243  concat
  concat(52,86)=5286  rev_concat(52,86)=8652  target=5286  concat
Conclude operator: concat.
Apply to (81, 77):  answer = 8177
Final: \boxed{8177}


### Task: numeral
### Problem:
Convert the Roman numeral XCIV to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  XC = 90  ->  0 + 90 = 90
  IV = 4  ->  90 + 4 = 94
Final: \boxed{94}


### Task: unit
### Problem:
Convert 76 litres to millilitres.
### Reasoning:
<|cot_start|>Conversion factor: 1 litres = 1000 millilitres.
So 76 litres = 76 * 1000 millilitres.
Compute step by step:
  7 * 10^1 * 1000 = 70000
  running total = 70000
  6 * 10^0 * 1000 = 6000
  running total = 76000
Final: \boxed{76000}


### Task: unit
### Problem:
Convert 48 metres to centimetres.
### Reasoning:
<|cot_start|>Conversion factor: 1 metres = 100 centimetres.
So 48 metres = 48 * 100 centimetres.
Compute step by step:
  4 * 10^1 * 100 = 4000
  running total = 4000
  8 * 10^0 * 100 = 800
  running total = 4800
Final: \boxed{4800}


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


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  45,15 -> 1545
  53,15 -> 1553
  17,54 -> 5417
Apply to: 93,96
### Reasoning:
<|cot_start|>Examples:
  45,15 -> 1545
  53,15 -> 1553
  17,54 -> 5417
Check both candidate forms:
  concat(45,15)=4515  rev_concat(45,15)=1545  target=1545  rev_concat
  concat(53,15)=5315  rev_concat(53,15)=1553  target=1553  rev_concat
  concat(17,54)=1754  rev_concat(17,54)=5417  target=5417  rev_concat
Conclude operator: rev_concat.
Apply to (93, 96):  answer = 9693
Final: \boxed{9693}


### Task: gravity
### Problem:
A mass of 20 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 = 20 * 981.
Step-by-step multiplication:
  2 * 10^1 * 981 = 19620
  running total = 19620
  0 * 10^0 * 981 = 0
  running total = 19620
So F = 19620 centiNewtons = 196.20 N.
Final: \boxed{196.20}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10010111 -> 00101111
  11010110 -> 10101101
  11100101 -> 11001011
Apply to: 10010001
### Reasoning:
<|cot_start|>Given examples:
  10010111 -> 00101111
  11010110 -> 10101101
  11100101 -> 11001011
Compare each bit position across the three examples:
  bit 0: 1,1,1 -> 0,1,1
  bit 1: 0,1,1 -> 0,0,1
  bit 2: 0,0,1 -> 1,1,0
  bit 3: 1,1,0 -> 0,0,0
  bit 4: 0,0,0 -> 1,1,1
  bit 5: 1,1,1 -> 1,1,0
  bit 6: 1,1,0 -> 1,0,1
  bit 7: 1,0,1 -> 1,1,1
Deduce rule: rotate left 1.
Apply to 10010001:
  result = 00100011
Final: \boxed{00100011}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  30,44 -> 1320
  55,94 -> 5170
  24,24 -> 576
Apply to: 58,51
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  30,44: '+' gives 74; target=1320  no
  30,44: '-' gives 14; target=1320  no
  30,44: '*' gives 1320; target=1320  MATCH
  30,44: 'concat' gives 3044; target=1320  no
  30,44: 'rev_concat' gives 4430; target=1320  no
  30,44: 'max*min+sum' gives 1394; target=1320  no
  30,44: 'digitsum2' gives 121; target=1320  no
  55,94: '+' gives 149; target=5170  no
  55,94: '-' gives 39; target=5170  no
  55,94: '*' gives 5170; target=5170  MATCH
  55,94: 'concat' gives 5594; target=5170  no
  55,94: 'rev_concat' gives 9455; target=5170  no
  55,94: 'max*min+sum' gives 5319; target=5170  no
  55,94: 'digitsum2' gives 529; target=5170  no
  24,24: '+' gives 48; target=576  no
  24,24: '-' gives 0; target=576  no
  24,24: '*' gives 576; target=576  MATCH
  24,24: 'concat' gives 2424; target=576  no
  24,24: 'rev_concat' gives 2424; target=576  no
  24,24: 'max*min+sum' gives 624; target=576  no
  24,24: 'digitsum2' gives 144; target=576  no
The only operator consistent with all examples is '*'.
Apply to (58, 51):
  result = 2958
Final: \boxed{2958}


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


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


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


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


### Task: numeral
### Problem:
Convert the Roman numeral LXI 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
Final: \boxed{61}


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


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10111110 -> 01000001
  11110010 -> 00001101
  10010010 -> 01101101
Apply to: 01111110
### Reasoning:
<|cot_start|>Given examples:
  10111110 -> 01000001
  11110010 -> 00001101
  10010010 -> 01101101
Compare each bit position across the three examples:
  bit 0: 1,1,1 -> 0,0,0
  bit 1: 0,1,0 -> 1,0,1
  bit 2: 1,1,0 -> 0,0,1
  bit 3: 1,1,1 -> 0,0,0
  bit 4: 1,0,0 -> 0,1,1
  bit 5: 1,0,0 -> 0,1,1
  bit 6: 1,1,1 -> 0,0,0
  bit 7: 0,0,0 -> 1,1,1
Deduce rule: invert (NOT).
Apply to 01111110:
  result = 10000001
Final: \boxed{10000001}


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


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


### Task: unit
### Problem:
Convert 55 minutes to seconds.
### Reasoning:
<|cot_start|>Conversion factor: 1 minutes = 60 seconds.
So 55 minutes = 55 * 60 seconds.
Compute step by step:
  5 * 10^1 * 60 = 3000
  running total = 3000
  5 * 10^0 * 60 = 300
  running total = 3300
Final: \boxed{3300}


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


### Task: 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: numeral
### Problem:
Convert the Roman numeral XXXVII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  X = 10  ->  0 + 10 = 10
  X = 10  ->  10 + 10 = 20
  X = 10  ->  20 + 10 = 30
  V = 5  ->  30 + 5 = 35
  I = 1  ->  35 + 1 = 36
  I = 1  ->  36 + 1 = 37
Final: \boxed{37}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  48,40 -> 4840
  75,65 -> 7565
  44,47 -> 4447
Apply to: 58,51
### Reasoning:
<|cot_start|>Examples:
  48,40 -> 4840
  75,65 -> 7565
  44,47 -> 4447
Check both candidate forms:
  concat(48,40)=4840  rev_concat(48,40)=4048  target=4840  concat
  concat(75,65)=7565  rev_concat(75,65)=6575  target=7565  concat
  concat(44,47)=4447  rev_concat(44,47)=4744  target=4447  concat
Conclude operator: concat.
Apply to (58, 51):  answer = 5851
Final: \boxed{5851}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  10,34 -> 340
  94,93 -> 8742
  48,91 -> 4368
Apply to: 33,31
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  10,34: '+' gives 44; target=340  no
  10,34: '-' gives 24; target=340  no
  10,34: '*' gives 340; target=340  MATCH
  10,34: 'concat' gives 1034; target=340  no
  10,34: 'rev_concat' gives 3410; target=340  no
  10,34: 'max*min+sum' gives 384; target=340  no
  10,34: 'digitsum2' gives 64; target=340  no
  94,93: '+' gives 187; target=8742  no
  94,93: '-' gives 1; target=8742  no
  94,93: '*' gives 8742; target=8742  MATCH
  94,93: 'concat' gives 9493; target=8742  no
  94,93: 'rev_concat' gives 9394; target=8742  no
  94,93: 'max*min+sum' gives 8929; target=8742  no
  94,93: 'digitsum2' gives 625; target=8742  no
  48,91: '+' gives 139; target=4368  no
  48,91: '-' gives 43; target=4368  no
  48,91: '*' gives 4368; target=4368  MATCH
  48,91: 'concat' gives 4891; target=4368  no
  48,91: 'rev_concat' gives 9148; target=4368  no
  48,91: 'max*min+sum' gives 4507; target=4368  no
  48,91: 'digitsum2' gives 484; target=4368  no
The only operator consistent with all examples is '*'.
Apply to (33, 31):
  result = 1023
Final: \boxed{1023}


### Task: unit
### Problem:
Convert 53 litres to millilitres.
### Reasoning:
<|cot_start|>Conversion factor: 1 litres = 1000 millilitres.
So 53 litres = 53 * 1000 millilitres.
Compute step by step:
  5 * 10^1 * 1000 = 50000
  running total = 50000
  3 * 10^0 * 1000 = 3000
  running total = 53000
Final: \boxed{53000}


### Task: gravity
### Problem:
A mass of 2 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 = 2 * 981.
Step-by-step multiplication:
  2 * 10^0 * 981 = 1962
  running total = 1962
So F = 1962 centiNewtons = 19.62 N.
Final: \boxed{19.62}


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


### Task: numeral
### Problem:
Convert the Roman numeral LXXIII 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
  I = 1  ->  71 + 1 = 72
  I = 1  ->  72 + 1 = 73
Final: \boxed{73}


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


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


### Task: gravity
### Problem:
A mass of 48 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 = 48 * 981.
Step-by-step multiplication:
  4 * 10^1 * 981 = 39240
  running total = 39240
  8 * 10^0 * 981 = 7848
  running total = 47088
So F = 47088 centiNewtons = 470.88 N.
Final: \boxed{470.88}


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


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


### Task: gravity
### Problem:
A mass of 14 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 14 * 981.
Step-by-step multiplication:
  1 * 10^1 * 981 = 9810
  running total = 9810
  4 * 10^0 * 981 = 3924
  running total = 13734
So F = 13734 centiNewtons = 137.34 N.
Final: \boxed{137.34}


### Task: gravity
### Problem:
A mass of 41 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 41 * 981.
Step-by-step multiplication:
  4 * 10^1 * 981 = 39240
  running total = 39240
  1 * 10^0 * 981 = 981
  running total = 40221
So F = 40221 centiNewtons = 402.21 N.
Final: \boxed{402.21}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00111010 -> 00011101
  10011010 -> 01001101
  00101111 -> 10010111
Apply to: 00110100
### Reasoning:
<|cot_start|>Given examples:
  00111010 -> 00011101
  10011010 -> 01001101
  00101111 -> 10010111
Compare each bit position across the three examples:
  bit 0: 0,1,0 -> 0,0,1
  bit 1: 0,0,0 -> 0,1,0
  bit 2: 1,0,1 -> 0,0,0
  bit 3: 1,1,0 -> 1,0,1
  bit 4: 1,1,1 -> 1,1,0
  bit 5: 0,0,1 -> 1,1,1
  bit 6: 1,1,1 -> 0,0,1
  bit 7: 0,0,1 -> 1,1,1
Deduce rule: rotate right 1.
Apply to 00110100:
  result = 00011010
Final: \boxed{00011010}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  72,99 -> 7299
  27,44 -> 2744
  36,57 -> 3657
Apply to: 11,46
### Reasoning:
<|cot_start|>Examples:
  72,99 -> 7299
  27,44 -> 2744
  36,57 -> 3657
Check both candidate forms:
  concat(72,99)=7299  rev_concat(72,99)=9972  target=7299  concat
  concat(27,44)=2744  rev_concat(27,44)=4427  target=2744  concat
  concat(36,57)=3657  rev_concat(36,57)=5736  target=3657  concat
Conclude operator: concat.
Apply to (11, 46):  answer = 1146
Final: \boxed{1146}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  82,61 -> 6182
  54,65 -> 6554
  43,59 -> 5943
Apply to: 31,26
### Reasoning:
<|cot_start|>Examples:
  82,61 -> 6182
  54,65 -> 6554
  43,59 -> 5943
Check both candidate forms:
  concat(82,61)=8261  rev_concat(82,61)=6182  target=6182  rev_concat
  concat(54,65)=5465  rev_concat(54,65)=6554  target=6554  rev_concat
  concat(43,59)=4359  rev_concat(43,59)=5943  target=5943  rev_concat
Conclude operator: rev_concat.
Apply to (31, 26):  answer = 2631
Final: \boxed{2631}


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


### Task: gravity
### Problem:
A mass of 49 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 49 * 981.
Step-by-step multiplication:
  4 * 10^1 * 981 = 39240
  running total = 39240
  9 * 10^0 * 981 = 8829
  running total = 48069
So F = 48069 centiNewtons = 480.69 N.
Final: \boxed{480.69}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  92,91 -> 8372
  99,90 -> 8910
  46,12 -> 552
Apply to: 18,68
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  92,91: '+' gives 183; target=8372  no
  92,91: '-' gives 1; target=8372  no
  92,91: '*' gives 8372; target=8372  MATCH
  92,91: 'concat' gives 9291; target=8372  no
  92,91: 'rev_concat' gives 9192; target=8372  no
  92,91: 'max*min+sum' gives 8555; target=8372  no
  92,91: 'digitsum2' gives 441; target=8372  no
  99,90: '+' gives 189; target=8910  no
  99,90: '-' gives 9; target=8910  no
  99,90: '*' gives 8910; target=8910  MATCH
  99,90: 'concat' gives 9990; target=8910  no
  99,90: 'rev_concat' gives 9099; target=8910  no
  99,90: 'max*min+sum' gives 9099; target=8910  no
  99,90: 'digitsum2' gives 729; target=8910  no
  46,12: '+' gives 58; target=552  no
  46,12: '-' gives 34; target=552  no
  46,12: '*' gives 552; target=552  MATCH
  46,12: 'concat' gives 4612; target=552  no
  46,12: 'rev_concat' gives 1246; target=552  no
  46,12: 'max*min+sum' gives 610; target=552  no
  46,12: 'digitsum2' gives 169; target=552  no
The only operator consistent with all examples is '*'.
Apply to (18, 68):
  result = 1224
Final: \boxed{1224}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  49,51 -> 5149
  98,19 -> 1998
  65,53 -> 5365
Apply to: 10,23
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  49,51: '+' gives 100; target=5149  no
  49,51: '-' gives 2; target=5149  no
  49,51: '*' gives 2499; target=5149  no
  49,51: 'concat' gives 4951; target=5149  no
  49,51: 'rev_concat' gives 5149; target=5149  MATCH
  49,51: 'max*min+sum' gives 2599; target=5149  no
  49,51: 'digitsum2' gives 361; target=5149  no
  98,19: '+' gives 117; target=1998  no
  98,19: '-' gives 79; target=1998  no
  98,19: '*' gives 1862; target=1998  no
  98,19: 'concat' gives 9819; target=1998  no
  98,19: 'rev_concat' gives 1998; target=1998  MATCH
  98,19: 'max*min+sum' gives 1979; target=1998  no
  98,19: 'digitsum2' gives 729; target=1998  no
  65,53: '+' gives 118; target=5365  no
  65,53: '-' gives 12; target=5365  no
  65,53: '*' gives 3445; target=5365  no
  65,53: 'concat' gives 6553; target=5365  no
  65,53: 'rev_concat' gives 5365; target=5365  MATCH
  65,53: 'max*min+sum' gives 3563; target=5365  no
  65,53: 'digitsum2' gives 361; target=5365  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (10, 23):
  result = 2310
Final: \boxed{2310}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  25,50 -> 1250
  83,42 -> 3486
  99,75 -> 7425
Apply to: 44,67
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  25,50: '+' gives 75; target=1250  no
  25,50: '-' gives 25; target=1250  no
  25,50: '*' gives 1250; target=1250  MATCH
  25,50: 'concat' gives 2550; target=1250  no
  25,50: 'rev_concat' gives 5025; target=1250  no
  25,50: 'max*min+sum' gives 1325; target=1250  no
  25,50: 'digitsum2' gives 144; target=1250  no
  83,42: '+' gives 125; target=3486  no
  83,42: '-' gives 41; target=3486  no
  83,42: '*' gives 3486; target=3486  MATCH
  83,42: 'concat' gives 8342; target=3486  no
  83,42: 'rev_concat' gives 4283; target=3486  no
  83,42: 'max*min+sum' gives 3611; target=3486  no
  83,42: 'digitsum2' gives 289; target=3486  no
  99,75: '+' gives 174; target=7425  no
  99,75: '-' gives 24; target=7425  no
  99,75: '*' gives 7425; target=7425  MATCH
  99,75: 'concat' gives 9975; target=7425  no
  99,75: 'rev_concat' gives 7599; target=7425  no
  99,75: 'max*min+sum' gives 7599; target=7425  no
  99,75: 'digitsum2' gives 900; target=7425  no
The only operator consistent with all examples is '*'.
Apply to (44, 67):
  result = 2948
Final: \boxed{2948}


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


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  29,22 -> 2922
  78,85 -> 7885
  87,66 -> 8766
Apply to: 50,32
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  29,22: '+' gives 51; target=2922  no
  29,22: '-' gives 7; target=2922  no
  29,22: '*' gives 638; target=2922  no
  29,22: 'concat' gives 2922; target=2922  MATCH
  29,22: 'rev_concat' gives 2229; target=2922  no
  29,22: 'max*min+sum' gives 689; target=2922  no
  29,22: 'digitsum2' gives 225; target=2922  no
  78,85: '+' gives 163; target=7885  no
  78,85: '-' gives 7; target=7885  no
  78,85: '*' gives 6630; target=7885  no
  78,85: 'concat' gives 7885; target=7885  MATCH
  78,85: 'rev_concat' gives 8578; target=7885  no
  78,85: 'max*min+sum' gives 6793; target=7885  no
  78,85: 'digitsum2' gives 784; target=7885  no
  87,66: '+' gives 153; target=8766  no
  87,66: '-' gives 21; target=8766  no
  87,66: '*' gives 5742; target=8766  no
  87,66: 'concat' gives 8766; target=8766  MATCH
  87,66: 'rev_concat' gives 6687; target=8766  no
  87,66: 'max*min+sum' gives 5895; target=8766  no
  87,66: 'digitsum2' gives 729; target=8766  no
The only operator consistent with all examples is 'concat'.
Apply to (50, 32):
  result = 5032
Final: \boxed{5032}


### Task: unit
### Problem:
Convert 50 kilograms to grams.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilograms = 1000 grams.
So 50 kilograms = 50 * 1000 grams.
Compute step by step:
  5 * 10^1 * 1000 = 50000
  running total = 50000
  0 * 10^0 * 1000 = 0
  running total = 50000
Final: \boxed{50000}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  24,49 -> 4924
  66,32 -> 3266
  24,16 -> 1624
Apply to: 68,77
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  24,49: '+' gives 73; target=4924  no
  24,49: '-' gives 25; target=4924  no
  24,49: '*' gives 1176; target=4924  no
  24,49: 'concat' gives 2449; target=4924  no
  24,49: 'rev_concat' gives 4924; target=4924  MATCH
  24,49: 'max*min+sum' gives 1249; target=4924  no
  24,49: 'digitsum2' gives 361; target=4924  no
  66,32: '+' gives 98; target=3266  no
  66,32: '-' gives 34; target=3266  no
  66,32: '*' gives 2112; target=3266  no
  66,32: 'concat' gives 6632; target=3266  no
  66,32: 'rev_concat' gives 3266; target=3266  MATCH
  66,32: 'max*min+sum' gives 2210; target=3266  no
  66,32: 'digitsum2' gives 289; target=3266  no
  24,16: '+' gives 40; target=1624  no
  24,16: '-' gives 8; target=1624  no
  24,16: '*' gives 384; target=1624  no
  24,16: 'concat' gives 2416; target=1624  no
  24,16: 'rev_concat' gives 1624; target=1624  MATCH
  24,16: 'max*min+sum' gives 424; target=1624  no
  24,16: 'digitsum2' gives 169; target=1624  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (68, 77):
  result = 7768
Final: \boxed{7768}


### Task: numeral
### Problem:
Convert the Roman numeral LXIX to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  X = 10  ->  50 + 10 = 60
  IX = 9  ->  60 + 9 = 69
Final: \boxed{69}


### Task: unit
### Problem:
Convert 21 metres to centimetres.
### Reasoning:
<|cot_start|>Conversion factor: 1 metres = 100 centimetres.
So 21 metres = 21 * 100 centimetres.
Compute step by step:
  2 * 10^1 * 100 = 2000
  running total = 2000
  1 * 10^0 * 100 = 100
  running total = 2100
Final: \boxed{2100}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  24,23 -> 2423
  89,80 -> 8980
  34,37 -> 3437
Apply to: 51,92
### Reasoning:
<|cot_start|>Examples:
  24,23 -> 2423
  89,80 -> 8980
  34,37 -> 3437
Check both candidate forms:
  concat(24,23)=2423  rev_concat(24,23)=2324  target=2423  concat
  concat(89,80)=8980  rev_concat(89,80)=8089  target=8980  concat
  concat(34,37)=3437  rev_concat(34,37)=3734  target=3437  concat
Conclude operator: concat.
Apply to (51, 92):  answer = 5192
Final: \boxed{5192}


### Task: gravity
### Problem:
A mass of 2 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 = 2 * 981.
Step-by-step multiplication:
  2 * 10^0 * 981 = 1962
  running total = 1962
So F = 1962 centiNewtons = 19.62 N.
Final: \boxed{19.62}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01011011 -> 10110110
  00000101 -> 00001010
  11011111 -> 10111111
Apply to: 11011100
### Reasoning:
<|cot_start|>Given examples:
  01011011 -> 10110110
  00000101 -> 00001010
  11011111 -> 10111111
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 1,0,1
  bit 1: 1,0,1 -> 0,0,0
  bit 2: 0,0,0 -> 1,0,1
  bit 3: 1,0,1 -> 1,0,1
  bit 4: 1,0,1 -> 0,1,1
  bit 5: 0,1,1 -> 1,0,1
  bit 6: 1,0,1 -> 1,1,1
  bit 7: 1,1,1 -> 0,0,1
Deduce rule: rotate left 1.
Apply to 11011100:
  result = 10111001
Final: \boxed{10111001}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  24,17 -> 196
  51,49 -> 361
  95,34 -> 441
Apply to: 18,96
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  24,17: '+' gives 41; target=196  no
  24,17: '-' gives 7; target=196  no
  24,17: '*' gives 408; target=196  no
  24,17: 'concat' gives 2417; target=196  no
  24,17: 'rev_concat' gives 1724; target=196  no
  24,17: 'max*min+sum' gives 449; target=196  no
  24,17: 'digitsum2' gives 196; target=196  MATCH
  51,49: '+' gives 100; target=361  no
  51,49: '-' gives 2; target=361  no
  51,49: '*' gives 2499; target=361  no
  51,49: 'concat' gives 5149; target=361  no
  51,49: 'rev_concat' gives 4951; target=361  no
  51,49: 'max*min+sum' gives 2599; target=361  no
  51,49: 'digitsum2' gives 361; target=361  MATCH
  95,34: '+' gives 129; target=441  no
  95,34: '-' gives 61; target=441  no
  95,34: '*' gives 3230; target=441  no
  95,34: 'concat' gives 9534; target=441  no
  95,34: 'rev_concat' gives 3495; target=441  no
  95,34: 'max*min+sum' gives 3359; target=441  no
  95,34: 'digitsum2' gives 441; target=441  MATCH
The only operator consistent with all examples is 'digitsum2'.
Apply to (18, 96):
  result = 576
Final: \boxed{576}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10011110 -> 01111001
  10100101 -> 10100101
  01100010 -> 01000110
Apply to: 10101001
### Reasoning:
<|cot_start|>Given examples:
  10011110 -> 01111001
  10100101 -> 10100101
  01100010 -> 01000110
Compare each bit position across the three examples:
  bit 0: 1,1,0 -> 0,1,0
  bit 1: 0,0,1 -> 1,0,1
  bit 2: 0,1,1 -> 1,1,0
  bit 3: 1,0,0 -> 1,0,0
  bit 4: 1,0,0 -> 1,0,0
  bit 5: 1,1,0 -> 0,1,1
  bit 6: 1,0,1 -> 0,0,1
  bit 7: 0,1,0 -> 1,1,0
Deduce rule: reverse bits.
Apply to 10101001:
  result = 10010101
Final: \boxed{10010101}


### Task: unit
### Problem:
Convert 22 days to hours.
### Reasoning:
<|cot_start|>Conversion factor: 1 days = 24 hours.
So 22 days = 22 * 24 hours.
Compute step by step:
  2 * 10^1 * 24 = 480
  running total = 480
  2 * 10^0 * 24 = 48
  running total = 528
Final: \boxed{528}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  78,92 -> 676
  27,63 -> 324
  53,26 -> 256
Apply to: 98,81
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  78,92: '+' gives 170; target=676  no
  78,92: '-' gives 14; target=676  no
  78,92: '*' gives 7176; target=676  no
  78,92: 'concat' gives 7892; target=676  no
  78,92: 'rev_concat' gives 9278; target=676  no
  78,92: 'max*min+sum' gives 7346; target=676  no
  78,92: 'digitsum2' gives 676; target=676  MATCH
  27,63: '+' gives 90; target=324  no
  27,63: '-' gives 36; target=324  no
  27,63: '*' gives 1701; target=324  no
  27,63: 'concat' gives 2763; target=324  no
  27,63: 'rev_concat' gives 6327; target=324  no
  27,63: 'max*min+sum' gives 1791; target=324  no
  27,63: 'digitsum2' gives 324; target=324  MATCH
  53,26: '+' gives 79; target=256  no
  53,26: '-' gives 27; target=256  no
  53,26: '*' gives 1378; target=256  no
  53,26: 'concat' gives 5326; target=256  no
  53,26: 'rev_concat' gives 2653; target=256  no
  53,26: 'max*min+sum' gives 1457; target=256  no
  53,26: 'digitsum2' gives 256; target=256  MATCH
The only operator consistent with all examples is 'digitsum2'.
Apply to (98, 81):
  result = 676
Final: \boxed{676}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  93,31 -> 9331
  14,31 -> 1431
  93,11 -> 9311
Apply to: 76,61
### Reasoning:
<|cot_start|>Examples:
  93,31 -> 9331
  14,31 -> 1431
  93,11 -> 9311
Check both candidate forms:
  concat(93,31)=9331  rev_concat(93,31)=3193  target=9331  concat
  concat(14,31)=1431  rev_concat(14,31)=3114  target=1431  concat
  concat(93,11)=9311  rev_concat(93,11)=1193  target=9311  concat
Conclude operator: concat.
Apply to (76, 61):  answer = 7661
Final: \boxed{7661}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  90,50 -> 9050
  19,54 -> 1954
  12,67 -> 1267
Apply to: 89,32
### Reasoning:
<|cot_start|>Examples:
  90,50 -> 9050
  19,54 -> 1954
  12,67 -> 1267
Check both candidate forms:
  concat(90,50)=9050  rev_concat(90,50)=5090  target=9050  concat
  concat(19,54)=1954  rev_concat(19,54)=5419  target=1954  concat
  concat(12,67)=1267  rev_concat(12,67)=6712  target=1267  concat
Conclude operator: concat.
Apply to (89, 32):  answer = 8932
Final: \boxed{8932}


### Task: unit
### Problem:
Convert 90 days to hours.
### Reasoning:
<|cot_start|>Conversion factor: 1 days = 24 hours.
So 90 days = 90 * 24 hours.
Compute step by step:
  9 * 10^1 * 24 = 2160
  running total = 2160
  0 * 10^0 * 24 = 0
  running total = 2160
Final: \boxed{2160}


### Task: gravity
### Problem:
A mass of 11 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 11 * 981.
Step-by-step multiplication:
  1 * 10^1 * 981 = 9810
  running total = 9810
  1 * 10^0 * 981 = 981
  running total = 10791
So F = 10791 centiNewtons = 107.91 N.
Final: \boxed{107.91}


### Task: gravity
### Problem:
A mass of 7 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 = 7 * 981.
Step-by-step multiplication:
  7 * 10^0 * 981 = 6867
  running total = 6867
So F = 6867 centiNewtons = 68.67 N.
Final: \boxed{68.67}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  84,29 -> 8429
  20,27 -> 2027
  29,80 -> 2980
Apply to: 33,62
### Reasoning:
<|cot_start|>Examples:
  84,29 -> 8429
  20,27 -> 2027
  29,80 -> 2980
Check both candidate forms:
  concat(84,29)=8429  rev_concat(84,29)=2984  target=8429  concat
  concat(20,27)=2027  rev_concat(20,27)=2720  target=2027  concat
  concat(29,80)=2980  rev_concat(29,80)=8029  target=2980  concat
Conclude operator: concat.
Apply to (33, 62):  answer = 3362
Final: \boxed{3362}


### Task: unit
### Problem:
Convert 91 days to hours.
### Reasoning:
<|cot_start|>Conversion factor: 1 days = 24 hours.
So 91 days = 91 * 24 hours.
Compute step by step:
  9 * 10^1 * 24 = 2160
  running total = 2160
  1 * 10^0 * 24 = 24
  running total = 2184
Final: \boxed{2184}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  32,18 -> 1832
  24,60 -> 6024
  39,47 -> 4739
Apply to: 90,23
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  32,18: '+' gives 50; target=1832  no
  32,18: '-' gives 14; target=1832  no
  32,18: '*' gives 576; target=1832  no
  32,18: 'concat' gives 3218; target=1832  no
  32,18: 'rev_concat' gives 1832; target=1832  MATCH
  32,18: 'max*min+sum' gives 626; target=1832  no
  32,18: 'digitsum2' gives 196; target=1832  no
  24,60: '+' gives 84; target=6024  no
  24,60: '-' gives 36; target=6024  no
  24,60: '*' gives 1440; target=6024  no
  24,60: 'concat' gives 2460; target=6024  no
  24,60: 'rev_concat' gives 6024; target=6024  MATCH
  24,60: 'max*min+sum' gives 1524; target=6024  no
  24,60: 'digitsum2' gives 144; target=6024  no
  39,47: '+' gives 86; target=4739  no
  39,47: '-' gives 8; target=4739  no
  39,47: '*' gives 1833; target=4739  no
  39,47: 'concat' gives 3947; target=4739  no
  39,47: 'rev_concat' gives 4739; target=4739  MATCH
  39,47: 'max*min+sum' gives 1919; target=4739  no
  39,47: 'digitsum2' gives 529; target=4739  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (90, 23):
  result = 2390
Final: \boxed{2390}


### Task: gravity
### Problem:
A mass of 18 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 18 * 981.
Step-by-step multiplication:
  1 * 10^1 * 981 = 9810
  running total = 9810
  8 * 10^0 * 981 = 7848
  running total = 17658
So F = 17658 centiNewtons = 176.58 N.
Final: \boxed{176.58}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  72,75 -> 5400
  41,65 -> 2665
  29,86 -> 2494
Apply to: 86,33
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  72,75: '+' gives 147; target=5400  no
  72,75: '-' gives 3; target=5400  no
  72,75: '*' gives 5400; target=5400  MATCH
  72,75: 'concat' gives 7275; target=5400  no
  72,75: 'rev_concat' gives 7572; target=5400  no
  72,75: 'max*min+sum' gives 5547; target=5400  no
  72,75: 'digitsum2' gives 441; target=5400  no
  41,65: '+' gives 106; target=2665  no
  41,65: '-' gives 24; target=2665  no
  41,65: '*' gives 2665; target=2665  MATCH
  41,65: 'concat' gives 4165; target=2665  no
  41,65: 'rev_concat' gives 6541; target=2665  no
  41,65: 'max*min+sum' gives 2771; target=2665  no
  41,65: 'digitsum2' gives 256; target=2665  no
  29,86: '+' gives 115; target=2494  no
  29,86: '-' gives 57; target=2494  no
  29,86: '*' gives 2494; target=2494  MATCH
  29,86: 'concat' gives 2986; target=2494  no
  29,86: 'rev_concat' gives 8629; target=2494  no
  29,86: 'max*min+sum' gives 2609; target=2494  no
  29,86: 'digitsum2' gives 625; target=2494  no
The only operator consistent with all examples is '*'.
Apply to (86, 33):
  result = 2838
Final: \boxed{2838}


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


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


### 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: equation
### Problem:
Discover the operator from examples then apply it:
  43,99 -> 4257
  18,67 -> 1206
  26,14 -> 364
Apply to: 95,22
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  43,99: '+' gives 142; target=4257  no
  43,99: '-' gives 56; target=4257  no
  43,99: '*' gives 4257; target=4257  MATCH
  43,99: 'concat' gives 4399; target=4257  no
  43,99: 'rev_concat' gives 9943; target=4257  no
  43,99: 'max*min+sum' gives 4399; target=4257  no
  43,99: 'digitsum2' gives 625; target=4257  no
  18,67: '+' gives 85; target=1206  no
  18,67: '-' gives 49; target=1206  no
  18,67: '*' gives 1206; target=1206  MATCH
  18,67: 'concat' gives 1867; target=1206  no
  18,67: 'rev_concat' gives 6718; target=1206  no
  18,67: 'max*min+sum' gives 1291; target=1206  no
  18,67: 'digitsum2' gives 484; target=1206  no
  26,14: '+' gives 40; target=364  no
  26,14: '-' gives 12; target=364  no
  26,14: '*' gives 364; target=364  MATCH
  26,14: 'concat' gives 2614; target=364  no
  26,14: 'rev_concat' gives 1426; target=364  no
  26,14: 'max*min+sum' gives 404; target=364  no
  26,14: 'digitsum2' gives 169; target=364  no
The only operator consistent with all examples is '*'.
Apply to (95, 22):
  result = 2090
Final: \boxed{2090}


### Task: gravity
### Problem:
A mass of 15 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 = 15 * 981.
Step-by-step multiplication:
  1 * 10^1 * 981 = 9810
  running total = 9810
  5 * 10^0 * 981 = 4905
  running total = 14715
So F = 14715 centiNewtons = 147.15 N.
Final: \boxed{147.15}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  39,10 -> 3910
  38,87 -> 3887
  59,27 -> 5927
Apply to: 42,91
### Reasoning:
<|cot_start|>Examples:
  39,10 -> 3910
  38,87 -> 3887
  59,27 -> 5927
Check both candidate forms:
  concat(39,10)=3910  rev_concat(39,10)=1039  target=3910  concat
  concat(38,87)=3887  rev_concat(38,87)=8738  target=3887  concat
  concat(59,27)=5927  rev_concat(59,27)=2759  target=5927  concat
Conclude operator: concat.
Apply to (42, 91):  answer = 4291
Final: \boxed{4291}


### Task: gravity
### Problem:
A mass of 20 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 = 20 * 981.
Step-by-step multiplication:
  2 * 10^1 * 981 = 19620
  running total = 19620
  0 * 10^0 * 981 = 0
  running total = 19620
So F = 19620 centiNewtons = 196.20 N.
Final: \boxed{196.20}


### Task: numeral
### Problem:
Convert the Roman numeral XXXII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  X = 10  ->  0 + 10 = 10
  X = 10  ->  10 + 10 = 20
  X = 10  ->  20 + 10 = 30
  I = 1  ->  30 + 1 = 31
  I = 1  ->  31 + 1 = 32
Final: \boxed{32}


### Task: gravity
### Problem:
A mass of 29 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 29 * 981.
Step-by-step multiplication:
  2 * 10^1 * 981 = 19620
  running total = 19620
  9 * 10^0 * 981 = 8829
  running total = 28449
So F = 28449 centiNewtons = 284.49 N.
Final: \boxed{284.49}


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


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01110111 -> 11101110
  10010001 -> 10001001
  10110001 -> 10001101
Apply to: 10100000
### Reasoning:
<|cot_start|>Given examples:
  01110111 -> 11101110
  10010001 -> 10001001
  10110001 -> 10001101
Compare each bit position across the three examples:
  bit 0: 0,1,1 -> 1,1,1
  bit 1: 1,0,0 -> 1,0,0
  bit 2: 1,0,1 -> 1,0,0
  bit 3: 1,1,1 -> 0,0,0
  bit 4: 0,0,0 -> 1,1,1
  bit 5: 1,0,0 -> 1,0,1
  bit 6: 1,0,0 -> 1,0,0
  bit 7: 1,1,1 -> 0,1,1
Deduce rule: reverse bits.
Apply to 10100000:
  result = 00000101
Final: \boxed{00000101}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01010110 -> 00000110
  00110100 -> 00000100
  01000110 -> 00000110
Apply to: 10111110
### Reasoning:
<|cot_start|>Given examples:
  01010110 -> 00000110
  00110100 -> 00000100
  01000110 -> 00000110
Compare each bit position across the three examples:
  bit 0: 0,0,0 -> 0,0,0
  bit 1: 1,0,1 -> 0,0,0
  bit 2: 0,1,0 -> 0,0,0
  bit 3: 1,1,0 -> 0,0,0
  bit 4: 0,0,0 -> 0,0,0
  bit 5: 1,1,1 -> 1,1,1
  bit 6: 1,0,1 -> 1,0,1
  bit 7: 0,0,0 -> 0,0,0
Deduce rule: and 0x0F.
Apply to 10111110:
  result = 00001110
Final: \boxed{00001110}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  68,86 -> 8668
  64,94 -> 9464
  85,41 -> 4185
Apply to: 10,56
### Reasoning:
<|cot_start|>Examples:
  68,86 -> 8668
  64,94 -> 9464
  85,41 -> 4185
Check both candidate forms:
  concat(68,86)=6886  rev_concat(68,86)=8668  target=8668  rev_concat
  concat(64,94)=6494  rev_concat(64,94)=9464  target=9464  rev_concat
  concat(85,41)=8541  rev_concat(85,41)=4185  target=4185  rev_concat
Conclude operator: rev_concat.
Apply to (10, 56):  answer = 5610
Final: \boxed{5610}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  22,52 -> 5222
  32,47 -> 4732
  23,67 -> 6723
Apply to: 67,35
### Reasoning:
<|cot_start|>Examples:
  22,52 -> 5222
  32,47 -> 4732
  23,67 -> 6723
Check both candidate forms:
  concat(22,52)=2252  rev_concat(22,52)=5222  target=5222  rev_concat
  concat(32,47)=3247  rev_concat(32,47)=4732  target=4732  rev_concat
  concat(23,67)=2367  rev_concat(23,67)=6723  target=6723  rev_concat
Conclude operator: rev_concat.
Apply to (67, 35):  answer = 3567
Final: \boxed{3567}