MathDB
Problems
Contests
International Contests
Lusophon Mathematical Olympiad
2022 Lusophon Mathematical Olympiad
2
2
Part of
2022 Lusophon Mathematical Olympiad
Problems
(1)
Fruits in a box
Source: Lusophon Mathematical Olympiad 2022 Problem 2
11/3/2022
Anselmo and Claudio are playing alternatively a game with fruits in a box. The box initially has
32
32
32
fruits. Anselmo plays first and each turn consists of taking away
1
1
1
,
2
2
2
or
3
3
3
fruits from the box or taking away
2
3
\frac{2}{3}
3
2
of the fruits from the box (this is only possible when the number of the fruits left in the box is a multiple of
3
3
3
). The player that takes away the last fruit from the box wins. Which of these two players has a winning strategy? How should that player play in order to win?
combinatorics
Game Theory