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.

(In reply to

Answer by K Sengupta)

t the outset, if possible let us assume that neither B nor C had grapes. Then, both the clues 2 and 3 are true, which is a contradiction as only one of the following four statements is true.

Thus, precisely one of B and C had grapes. If B had grapes, then clues 2 and 4 are true. This is a contradiction.

Accordingly, C must have had grapes. Hence, the third statement is true and since precisely one of the statements is true, it follows that the remaining statements are all false.

Since statement 4 is false, it now follows that B had apples, so that A had bananas.