Problem

Source: 2021 Dürer Math Competition Finals Day 1 E6 E+6

Tags: combinatorics, game



(Game) In an Indian reservatory there are $15$ totem poles arranged according to the left figure. Silent Stream and Red Fire used to play the following game: In turns they stretch ropes between two-two poles in such a way that every stretched rope is parallel to a side of the big triangle and no rope can go along a pole that is already touched by another rope. Furthermore, if instead of a rope one can stretch out a straight line extension of the rope, then one should stretch out this extension. The one who cannot stretch out more rope according to the rules loses. Win two games in a row against the organizers! You can decide that you want to start or to be the second player. The figure on the right depicts the first three steps of a game. First Silent Stream stretches the blue rope, then Red Fire stretches the red one, finally Silent Stream stretches the blue one.