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Problem 3 of Third round

Source: VII International Festival of Young Mathematicians Sozopol 2016, Theme for 10-12 grade

September 1, 2019
combinatorial geometrycombinatorics

Problem Statement

Let A1A2…A66A_1 A_2…A_{66} be a convex 66-gon. What’s the greatest number of pentagons AiAi+1Ai+2Ai+3Ai+4,1≤i≤66,A_i A_{i+1} A_{i+2} A_{i+3} A_{i+4},1\leq i\leq 66, which have an inscribed circle? (A66+i≡AiA_{66+i}\equiv A_i).
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