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Mathematics Goes to the Movies

by Burkard Polster and Marty Ross

Last Year in Marienbad (1961)

Mysterious guy (M) introduces a Nimlike game that he always wins.
15:00
M: I know a game I always win.
O(ther): If you can’t lose, it’s no game.
M: I can lose, but I always win.
O: Let’s try it.
M: Two people play. The cards are laid out like this. Seven, five, three, one. Each player can pick up as many cards as he likes but only from one row each time. The player who picks up the last card is the loser. Will you start?
Notation: x, y (x in 1,3,5,7 tells which row, y tells how many are taken)
O 7 1
M 5 1
O 7 6
M 5 2
O 5 1
M 3 2
O 1 1
M 3 1

7 1
5 1
7 6
5 2
5 1
3 2 and he wins

Just for fun
21:00
two games
Other guy starts again
O 1 1
M 3 1
O 7 1
M 5 1
O 5 1
M 7 1
O 3 1
M 7 3
O 5 1
M 3 1
O 7 1
M 5 2 and wins
This time the mysterious guy starts

What if you play first?
M 1 1
O 3 1
M 5 1
O 3 1
M 7 2
O 3 1
M 7 1
O 7 1
M 5 1
O 7 1
M 5 1
O 7 1
M 5 2 and wins

37:00
in passing

1:12:30
Different onlookers speculating
It’s a silly game.
You have to know the trick.
Simply take an odd number.
There must be rules.
The beginner always loses.
I’m sure Frank played that game last year.
You must play on the basis of seven.
O: Begin now, please.
M: With pleasure. Which one would you like me to take?
O: That one.
M 7 1
O 5 2
M 7 5
O 3 2
M 5 3 and wins (three left on the table in different rows)
O: Well, I’ve lost. 1:15:00