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160 sats \ 0 replies \ @SimpleStacker 1 Nov \ on: [Daily puzzle] Truth-tellers and liars science
For a bit of fun, we can work through an entire table. The first three columns are the actual types of each person. The next three columns are whether their statements are True or False. The last column shows which statements are a contradiction to their type.
| T(A) | T(B) | T(C) | S(A) | S(B) | S(C) | Contradiction |
|---|---|---|---|---|---|---|
| T | T | T | T | F | T | B |
| T | T | L | T | T | F | None |
| T | L | T | F | F | T | A |
| T | L | L | F | T | F | A,B |
| L | T | T | F | T | F | C |
| L | T | L | F | F | T | B,C |
| L | L | T | T | T | F | A,B,C |
| L | L | L | T | F | T | A,C |
So there's only one configuration with no contradictions and that's Alice and Bob are truth tellers and Carol is a liar.
Interestingly, there's only one configuration in which all three statements are contradictions to their type.