MathDB

4

Part of 2020 Spain Mathematical Olympiad

Problems(1)

Adding game.

Source: Spain Mathematical Olympiad 2020 P4

7/15/2020
Ana and Benito play a game which consists of 20202020 turns. Initially, there are 20202020 cards on the table, numbered from 11 to 20202020, and Ana possesses an extra card with number 00. In the kk-th turn, the player that doesn't possess card kāˆ’1k-1 chooses whether to take the card with number kk or to give it to the other player. The number in each card indicates its value in points. At the end of the game whoever has most points wins. Determine whether one player has a winning strategy or whether both players can force a tie, and describe the strategy.
Spaincombinatoricsgame