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Show existence of method to buy 9 tickets.

Source:

December 31, 2011
combinatorics unsolvedcombinatorics

Problem Statement

In a lottery, a person must select six distinct numbers from 1,2,3,…,361, 2, 3,\dots, 36 to put on a ticket. The lottery commitee will then draw six distinct numbers randomly from 1,2,3,…,361, 2, 3, \ldots, 36. Any ticket with numbers not containing any of these 66 numbers is a winning ticket. Show that there is a scheme of buying 99 tickets guaranteeing at least one winning ticket, but 88 tickets are not enough to guarantee a winning ticket in general.
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