There are 3 cans containing different foods.
Nuts in one can.
Sliced Peaches in juices in another and the third can contains sliced oranges in juices.
Someone has steamed off and switched the labels of all the cans so every can will have a label that is not the actual food inside it.
Can you figure out which cans contain which foods without opening any?
Let the denote the can with the nut label, sliced peach label and sliced oranges in juices label respectively as C(n), C(sp) and C(soj)
At the outset, we shake the cans. The one that rattles must be the can with the nuts. It cannot be C(n). So it must be either C(sp) or C(soj).
Without loss of generality, assume that C(sp) contains the nuts. Then C(soj) cannot contain sliced oranges, and accordingly, C(soj) must contain sliced peaches. C(n) will therefore contain sliced oranges in juices.
However, if C(soj) contains the nuts, then arguing as before, we observe that:
C(sp) will contain the nuts and sliced oranges and C(n) contains sliced peaches.
Edited on July 20, 2022, 12:19 am
Puzzle Solution
