6 holes from punches in the buses of a certain bus company
Source: 2005 Estonia National Olympiad Final Round grade 12 p1
April 13, 2020
combinatorics
Problem Statement
Punches in the buses of a certain bus company always cut exactly six holes into the ticket. The possible locations of the holes form a table as shown in the figure. Mr. Freerider wants to put together a collection of tickets such that, for any combination of punch holes, he would have a ticket with the same combination in his collection. The ticket can be viewed both from the front and from the back. Find the smallest number of tickets in such a collection.
https://cdn.artofproblemsolving.com/attachments/b/b/de5f09317a9a109fbecccecdc033de18217806.png