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UKMT Senior Kangaroo, 2022

Combinatorics Difficulty 3.0 AMC 10/12 Prove it United Kingdom

Zia conducted a study of the number of coins each member of her club had in their pocket. To her surprise, nobody had zero coins and exactly seven people had only one coin each. Everybody else had at least two coins. She drew a pie chart of her results, and to her surprise found each sector had an angle which was an integer ten degrees larger than its immediate predecessor. The smallest sector in the pie chart had an angle of $35^\circ$ . How many people are in Zia's club?

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