Gimme The Money

Probability Level 2

Two players play a game according to the following rules:

  • They place three heaps of coins on a table. The first heap has 1010 coins, the second heap has 77 coins, and the third heap has 99 coins.

  • The second player adds another pile of coins on the table, having at most 1010 coins.

  • The players take turns alternately, starting with the first player. At each move, the player has to remove a positive number of coins from one heap. The player who removes the last coin wins.

It turns out that regardless of the strategy of the first player, the second player always wins with optimal play. How many coins should the second player add in the fourth pile?

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