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You and a friend play a game where you start with a pile of 1000 stones

+1 vote
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You and a friend play a game where you start with a pile of 1000 stones, and each turn you can either add 2 stones to the pile or remove 10 stones.

The player to remove the last stone wins.

Should you start first or second to win this game?

posted Jun 24, 2017 by anonymous

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1 Answer

+1 vote

If we start 2nd and copy every move that the 1st guy does then the game will either never end or will make you a winner.

answer Jun 24, 2017 by Tejas Naik



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Consider a two player coin game where each player gets turn one by one. There is a row of even number of coins, and a player on his/her turn can pick a coin from any of the two corners of the row. The player that collects coins with more value wins the game. Develop a strategy for the player making the first turn, such he/she never looses the game?

Note that the strategy to pick maximum of two corners may not work. In the following example, first player looses the game when he/she uses strategy to pick maximum of two corners.

Example
  18 20 15 30 10 14
First Player picks 18, now row of coins is
  20 15 30 10 14
Second player picks 20, now row of coins is
  15 30 10 14
First Player picks 15, now row of coins is
  30 10 14
Second player picks 30, now row of coins is
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First Player picks 14, now row of coins is
  10 
Second player picks 10, game over.

The total value collected by second player is more (20 + 
30 + 10) compared to first player (18 + 15 + 14).
So the second player wins. 
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