The owner of a fruit orchard has collected three barrels of fruit. There is one barrel of apples, one barrel of pears and one barrel that contains a mixture of apples and pears.

The barrels are all labelled. One label reads “apples”, another reads “pears” and the other reads “apples and pears”. Unfortunately, none of the three barrels are labelled correctly!

You can take out and look at just one piece of fruit from one of the barrels. How can you determine what each of the barrels contain?

If you choose to inspect a piece of fruit from the barrel labelled “apples and pears”, you can be sure that it will contain either only apples or pears (since you know that all barrels are labelled incorrectly). Looking at the fruit will of course tell you which barrel it is.

The other two barrels will be labelled “apples” and “pears”. If the piece of fruit you looked at earlier was an apple, you can be sure that the barrel labelled “apples” will contain pears and the barrel labelled “pears” will contain both apples and pears.

If however the piece of fruit you looked at earlier was a pear, you can be sure that the barrel labelled “pears” will contain apples and the barrel labelled “apples” will contain both apples and pears.