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Harvard-MIT Mathematics Tournament, Team Round B

Combinatorics Difficulty 4.4 AIME Find the answer United States

Problem:
Suppose we have a regular hexagon and draw all its sides and diagonals. Into how many regions do the segments divide the hexagon? (No proof is necessary.)

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:
An accurate diagram and a careful count yields the answer.

Answer: $24$

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.