A Thinking Game Using Multiples of Four
Arrange 12 pennies in a circle around a nickel.
The game is played between two players (Player A and Player B). Player A is instructed
to remove either1, 2, or 3 pennies from the circle. Then when it is Player B’s turn he/she
will also remove either1, 2, or 3 pennies. The game continues until the last coin left is
the nickel. The player who is forced to remove the nickel at the last turn loses the game.
Hint: When there are only four pennies left, a wise, observant player will realize that the
first player to remove 1, 2, or 3 of the remaining coins will leave the last player with the
option to remove all but the nickel which then forces the last player to take the nickel,
therefore losing the game. Eventually one will realize that if you always try to remove
multiples of four at each pair of moves, then Player B (the one with the second turn) can
always win.
Example: If Player A takes one coin then Player B should take 3 since that makes the
first set of 4. Then if Player A takes 2 then Player B should take 2 thus making another
set of 4. The game continues until Player B wins. If Player B figures out the object of
the game but must start with the first move, it would be smart to only take one coin
hoping that Player A would take 1 or 2 allowing you the opportunity to become the
player who can make a set of four in the third move. For a bigger challenge try placing
16 or 20 pennies around the nickel. The object is still to remove sets of four even though
each player can only choose to remove 1, 2, or 3 coins at a time. Try it! It’s so fun to
watch the students as they eventually catch on.