HMMT 二月 2022 · 冲刺赛 · 第 6 题

HMMT February 2022 — Guts Round — Problem 6

[6] Regular polygons ICAO , V EN T I , and ALBEDO lie on a plane. Given that IN = 1, compute the number of possible values of ON .

解析

[6] Regular polygons ICAO , V EN T I , and ALBEDO lie on a plane. Given that IN = 1, compute the number of possible values of ON . Proposed by: Sean Li Answer: 2 Solution: First, place ALBEDO . We then note that ICAO has two orientations, both of which have I on EO . Next, we note that for any given orientation of ICAO , the two orientations of V EN T I have N symmetric to line EI . Thus, for any given orientation of ICAO , we have that ON is the same in both orientations of V EN T I , which gives a total of 2 possible values for ON .