HMMT 十一月 2020 · 冲刺赛 · 第 34 题

HMMT November 2020 — Guts Round — Problem 34

[20] Let a be the proportion of teams that correctly answered problem 1 on the Guts round. Estimate A = b 10000 a c . An estimate of E earns max(0 , b 20 − | A − E | / 20 c ) points. If you have forgotten, question 1 was the following: Two hexagons are attached to form a new polygon P . What is the minimum number of sides that P can have?

解析

[20] Let a be the proportion of teams that correctly answered problem 1 on the Guts round. Estimate A = b 10000 a c . An estimate of E earns max(0 , b 20 −| A − E | / 20 c ) points. If you have forgotten, question 1 was the following: Two hexagons are attached to form a new polygon P . What is the minimum number of sides that P can have? Proposed by: Daniel Zhu Answer: 2539 Solution: 689 teams participated in the guts round. Of these, • 175 teams submitted 3, the correct answer; • 196 teams submitted 4; • 156 teams submitted 10 (the correct answer if the hexagons had to be regular); • 64 teams submitted 6 (the correct answer if one of the hexagons had to be regular); • 19 teams submitted 8 (the correct answer if the hexagons had to be convex); • 17 teams submitted 11; • 13 teams submitted other incorrect answers; • 49 teams did not submit an answer.