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MIcompany Puzzle: Counting Riddle Matches

MIcompany
02 March 2020
Puzzle

Puzzle by MIcompany

The game Nim is played with 2 players and a stack of x matches. In turn, the players can take 1, 2 or 3 matches from the pile. The player who takes the last match wins. Suppose that the players start with a stack of 3 matches, then there are 4 possible game runs (the numbers shown represent the number of matches on the pile):

3 à 0
3 à1 à 0
3 à 2 à 0
3 à 2 à 1 à 0

How many play runs are there when the players start with 6 matches? A move does not have to be tactical, as long as it is legal.

Hint: it is possible to explicitly explain the game progress, but there is a certain pattern in which it can also be faster.

Read A week in the life of Sven Oldenburger for the solution!

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