A box contains apples oranges and pears How many fruits must

A box contains apples, oranges, and pears. How many fruits must you pick from the box to guarantee that you have at least two fruits of the same type?

Solution

If you pick m fruits which contains q1apples,q2 oranges,,q3 of pears.

Then m =q1+q2+q3 , and you want at least one of q1,q2,q3 to at least 2

. By the average principle, if m/3>1, then at least one of q1,q2,q3 is greater than 1 (thus at least 2).

Thus m = 4