4. In a box, there is a large batch of flowers of six types mixed together. Vasya randomly takes flowers one by one from the box. As soon as he collects 5 flowers of the same type, he makes a bouquet and sells it. What is the minimum number of flowers he needs to take to guarantee selling 10 bouquets?
Answer: 70.

Solution. Note that 69 flowers are not enough. Indeed, if Vasya pulled out 49 flowers of the first type and 4 flowers of each of the other types, then in total he took $49+5 \cdot 4=69$ flowers, but from them, he can only make 9 bouquets.

Suppose Vasya pulled out the 70th flower and possibly sold one bouquet. From the remaining flowers, it is impossible to form another bouquet. Therefore, Vasya has no more than four flowers of each type, and in total,
no more than 24 flowers. Since both 70 and the number of sold flowers are multiples of 5, no more than 20 flowers could remain. This means Vasya sold at least 50 flowers, that is, 10 bouquets.