1. A new series of "Kinder Surprises" - chocolate eggs, each containing a toy car - was delivered to the store. The seller told Pete that there are only five different types of cars in the new series, and it is impossible to determine which car is inside by the appearance of the egg. What is the minimum number of "Kinder Surprises" Pete should buy to guarantee having three cars of the same type, regardless of which type?
Solution. If Petya buys 10 "Kinder Surprises," in the least favorable situation for him, he will get two cars of each type. If he buys 11 "Kinder Surprises," he will get three cars of one type. Let's prove this. Suppose Petya bought 11 "Kinder Surprises" but did not get three cars of one type. This means the number of cars is no more than 10 (two cars of one type, a total of five types). Contradiction.

Answer. Petya should buy no fewer than 11 "Kinder Surprises."