Est. 1998 — 27 years of woodworking knowledge
Tuesday puzzle
Alex Y
Two boxes are labeled "A" and "B". A sign on box A says "The sign on box B is true and the gold is in box A". A sign on box B says "The sign on box A is false and the gold is in box A".
Part I: Assuming there is gold in one of the boxes, which box contains
the gold?
Part II: Can you identify an assumption that you implicitly made to get your answer in Part I?
Tough problem!
Bill Earl
I consulted two PhD's. Even the pair-o-doc's couldn't figure it out.
Alex Y
Very good! I didn't see that possibility. Maybe you can write up an explanation after everyone has had a day to work on it?
Re: Tuesday puzzle
Gary Smyth
I'm saying the gold is in "B". If "A is true then "B" is true and the gold is in "A. If "A is false then B" is true or false so the question rests on "B" and "A" has to be false. So the statement on B is false or the gold is in "B" so either choice means the gold is in "B".
That's the answer I got
Alex Y
with a slightly different (but obviously equivalent) chain of reasoning. I'll let Bill explain the assumption we made, since he saw it on his own, so can probably explain it better than I.
Re: That's the answer I got
Bill Earl
I think that the assumption you made is that one of the statements has to be true. This is basically a slightly more convoluted form of the "liars paradox" and nothing can be logically deduced from it.
or, in it's simplest form:
Re: That's the answer I got
Alex Y
I think that the assumption you made is that one of the statements has to be true.
If the gold is in Box A, then the statements reduce to what you have here:
This is basically a slightly more convoluted form of the "liars paradox" and nothing can be logically deduced from it.
A: Statement B is true.
B: Statement A is false.
If the gold is in Box B, then both statements are false, since both claim that it is in Box A; it doesn't matter what statement is "anded" to that.