MathDB

Some lottery is played as follows. A lottery participant buys a card with

10

numbered cells. He has the right to cross out any

4

of these

10

cells. Then a drawing occurs, during which some

7

out of

10

cells become winning. The player wins when all

4

squares he crosses out are winning. The question arises, what is the smallest number of cards that can be used so that, if filled out correctly, at least one of these cards will win in any case? We do not suggest that you answer this question (we ourselves do not know the answer), although, of course, we will be very glad if you do and will evaluate this achievement accordingly. The task is; to indicate a certain number

n

and a method of filling n cards that guarantees at least one win. The smaller

n

, the higher the rating of the work.

Problem Statement