Question

Suppose that 100 lottery tickets are given out in sequence to the first 100 guests to arrive at a party. Of these 100 tickets, only 11 are winning tickets. The generalized pigeonhole principle guarantees that there must be a streak of at least l losing tickets in a row. Find l.

Answer 1

L = 8 losing tickets in a row

Explanation:

Since there are 11 winning tickets out of 100. This problem can be treated as spreading out 89 losing tickets over 12 intervals (before the first, after the last and between each winning ticket).

`L=(89)/(12) = 7.42`

Since the minimum possible streak found is not a whole number of tickets, it must be rounded up to the next whole number.

Thus, the minimum losing streak L is 8 losing tickets in a row.