A, B and C just finished their breakfast. One of the boys had apples, another bananas and the third, grapes. If only one of the following four statements is true, who had what for breakfast?

C had bananas.

C did not have grapes.

B did not have grapes.

B did not have apples.

The key, I believe, is what B ate.

If B ate bananas, both of the latter 2 statements are true. Since one and only one of the statements can be true, that cannot be the case.
B must have eaten grapes or apples.
That means, then, that of the third and fourth statements, one of them is true and the other false. Consequently, both of the first two statements are false, most namely the second one, and C did indeed have grapes for breakfast.
Since B didn't have the bananas, and C had grapes, A must have had the bananas.
That leaves the apples for B.

In short:
A - bananas
B - apples
C - grapes

Interestingly to note, the problem can be solved without considering the first statement at all.

Posted by DJ on 2003-03-03 18:23:34