GOLD COIN GAME MA 201

Number of Players: 2

Materials Needed: As many coins as you want to have. For today’s game, we are going to use 27 coins.

In general, we will see what the “pattern” looks like with n coins.

Rules of the Game: You are competing with the other person. Therefore, place the pile of coins directly

between the two players. Pick one of the two people to take a turn first. During a turn, a player must remove

1, 2, or three coins from the pile. Once a player has removed coins, the turn is over. The other player will

then take their turn in removing coins from the pile. The players continue to take turns until all of the coins

have been taken.

Conclusion of Game: The winner of the game is the last person to remove coins from the pile.

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

Working BackwardsThe objective of the above game was to be the last person to take the coins from the pile. Is there a way

to ensure that you will always be that last person? To see if there is, we will work backwards through the

problem. Follow the chart below, which shows how many coins there should be for each player from the end

to the beginning.

Yourself Other Player

End of Game Want to have 1-3 coins left to take (so you

can win)

Should have 4 (no other option for them)

Want 5, 6 or 7 coins (so opponent gets 4)

Should have 8 (no other option for them)

Want 9, 10 or 11 coins (so opponent gets 8)

Should have 12 (no other option for them)...

...

Should have 24 (no other option for them)

Beginning of Game Start with 27 coins - take 3

1 October 1, 2007