MathDB
Combinatorics

Source: 2024 KJMO first round

October 27, 2024
combinatorics

Problem Statement

As shown in the following figure, there is a line segment consisting of five line segments AB,BC,CD,DE,andEAAB, BC, CD, DE, and EA and 1010 intersection points of these five line segments. Find the number of ways to write 11 or 22 at each of the 1010 vertices so that the following conditions are satisfied.
ā˜…\bigstar The sum of the four numbers written on each line segment AB,BC,CD,DE,andEAAB, BC, CD, DE, and EA is the same.
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