[Daily puzzle] Truth-tellers and liars \ stacker news ~science

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630 sats \ 6 comments \ @south_korea_ln 1 Nov science

Following @0xbitcoiner's suggestion to have puzzles with a more real context (#743441), here a try at something in that direction:

On a remote island, there are two types of people: truth-tellers, who always tell the truth, and liars, who always lie. You meet three people on this island: Alice, Bob, and Carol.

Alice says, "Bob and I are of the same type." Bob says, "Alice and Carol are of opposite types." Carol says, "Alice and I are of the same type."

Determine who the truth-tellers and liars are.

Previous iteration: #748120 (partial solution in #748556).

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160 sats \ 0 replies \ @SimpleStacker 1 Nov

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.

250 sats \ 0 replies \ @Roll 1 Nov

truth-tellers: Alice and Bob

liars: Carol

125 sats \ 0 replies \ @senf 1 Nov

Alice and Bob are truth-tellers, Carol is a liar.

42 sats \ 2 replies \ @Aardvark 1 Nov

Alice and Bob are honest. Carol is full of shit.

Also 42.

10 sats \ 1 reply \ @south_korea_ln OP 1 Nov

42 sats for you, every time, until the answer is actually 42.

0 sats \ 0 replies \ @Aardvark 1 Nov

I suspect that yesterday's was actually 42, but I have no way to prove it....