Everything Depends On The Other Player

Logic Level 2

Chip Removal is a game between players I and II.

  • There is a pile of 1400 chips in the center of a table.
  • A move consists of removing exactly 1, 3, 5, or 7 chips from the pile.
  • Players alternate moves with Player I starting.
  • The player that removes the last chip wins.

Which player has a winning strategy?

Need help check Take-away game 1 .
Player I Player II Neither player has a winning strategy

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Mohamed Hassan by Mohamed Hassan , 25, Egypt

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3 solutions

Vasu Bansal
Jun 2, 2016

player 2 will win as after every move parity(even or odd) changes. 0 is even and so is 1400. after every move of 1 the no of chips will be odd but at the end of every move of 2 it will be even

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Wojciech Bochenek
May 25, 2016

Since there is an even number of chips, and you can only take away an odd number, that means you would need two odd numbers like 3+3 to make 6. Thus the 1st player takes away the 3 and then the second player completes the pattern and takes away another three to be left with 6 pieces taken. Now you repeat until the second player finally takes away the last piece

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Owen Berendes
Jun 2, 2016

1400 is evenly divisible by 8. As long as player 2 takes 8-x where x is player one's previous move player 2 will always remove the last chip.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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