Cosmo plays the following (single-player) game with three wooden sticks:
- He first checks whether he can form a triangle from the three sticks (which means: whether the longest stick is at most as long as the combined length of the two shorter sticks).
- If Cosmo can form such a triangle: Cosmo has won the game.
- If Cosmo cannot form such a triangle: Cosmo takes the longest stick, cuts off from it a piece as long as the combined length of the two shorter sticks, throws away this piece, and keeps the remaining shortened stick.
- Then Cosmo repeats these steps with the two shorter sticks and the shortened stick.
Will Cosmo always win the game after a finite number of steps? For any choice of wooden sticks to start with?