MathDB

The integers from

1

100

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

10

of these

100

numbers. Then 10 of the integers from

1

100

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

13

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

12

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

Problem Statement