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Problems
Contests
National and Regional Contests
The Philippines Contests
Philippine MO
2016 Philippine MO
4
4
Part of
2016 Philippine MO
Problems
(1)
2, 4, 5-Nim
Source: Philippines MO 2016/4
1/21/2017
Two players,
A
A
A
(first player) and
B
B
B
, take alternate turns in playing a game using 2016 chips as follows: the player whose turn it is, must remove
s
s
s
chips from the remaining pile of chips, where
s
ā
{
2
,
4
,
5
}
s \in \{ 2,4,5 \}
s
ā
{
2
,
4
,
5
}
. No one can skip a turn. The player who at some point is unable to make a move (cannot remove chips from the pile) loses the game. Who among the two players can force a win on this game?
combinatorics
game
nim