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12 numbered chairs arranged in a circle

Source: 2019 Dürer Math Competition Finals Day2 E+13 https://artofproblemsolving.com/community/c1621835_2019_

January 5, 2022
combinatorics

Problem Statement

There are 1212 chairs arranged in a circle, numbered from 1 1 to 12 12. How many ways are there to select some of the chairs in such a way that our selection includes 33 consecutive chairs somewhere?
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