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Cofferwit

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Every member forges vaults: the server draws a secret code, and the forger picks a few true statements that point to it alone, as few as possible. The other members pick them later, in 3 attempts and a few minutes. A vault that holds pays its forger, a vault that gives way pays the thief.

A sample vault

bronze vault, 4 digits, 5 clues. Find the code.

  1. A is odd
  2. A + B is 15
  3. A + D is 10
  4. the difference between C and D is 1
  5. A + C is less than B + D
Notebook: tick a digit to cross it out (nothing is sent)
ABCD
0
1
2
3
4
5
6
7
8
9
See the solution

Code: 7823

  1. Clue 1: A is odd, so A is 1, 3, 5, 7 or 9.
  2. Clue 2: A + B is 15, so A is 7 or 9 and B is 6 or 8.
  3. Clue 3: A + D is 10, so D is 1 or 3.
  4. Clue 4: the difference between C and D is 1, so C is 0, 2 or 4.
  5. Clue 5: A + C is less than B + D, so C is not 4.
  6. Hypothesis: if A were 9, then B = 6 and D = 1, and clue 5 could no longer be true.
  7. So A = 7.
  8. Clue 2: A + B is 15, so B = 8.
  9. Clue 3: A + D is 10, so D = 3.
  10. Clue 4: the difference between C and D is 1, so C = 2.
  11. The code is 7823.

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