# Cutting A Very Large Polygon

**Logic**Level 3

Dan and Sam play a game on a regular polygon of 100 sides. Each one draws a diagonal on the polygon in his turn.

When someone draws a diagonal, it cannot have common points (except the vertexes of the polygon) with other diagonals already drawn.

The game finishes when someone can't draw a diagonal on the polygon following the rules; that person is the loser. If Dan begins, who will win? In other words, who has a winning strategy?

**Clarification:** The diagonals of a polygon are straight lines that join non-adjacent vertexes.

###### This is the thirteenth problem of the set Winning Strategies.

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