MathDB

The integers from

1

36

are written on a “mathlotto” ticket. When you buy a “mathlotto” ticket, you choose

6

of these

36

numbers. Then

6

of the integers from

1

36

are drawn, and a winning ticket is one which does not contain any of them. Prove that
(a) if you buy

9

tickets, you can choose your numbers so that regardless of which numbers are drawn, you are guaranteed to have at least one winning ticket;
(b) if you buy only

8

tickets, it is possible for you not to have any winning tickets, regardless of how you choose your numbers.
(S Tokarev)

Problem Statement