MathDB

Given a positive integer

n\ge 3

, Arándano and Banana play a game. Initially, numbers

1,2,3,\dots,n

are written on the blackboard. Alternatingly and starting with Arándano, the players erase numbers from the board one at a time, until exactly three numbers remain on the board. Banana wins the game if the last three numbers on the board are the sides of a nondegenerate triangle, and Arándano wins otherwise. Determine, in terms of

n

, who has a winning strategy.

Problem Statement