Rules

In the Game of Fifteen, two players take turns choosing numbers according to the following rules.

  1. Each player takes turns choosing a whole number greater than \(0\) and less than \(10\).
  2. Once a number has been chosen, it cannot be chosen again.
  3. The first player to collect three numbers that add up to \(15\) wins.
  4. If all the numbers have been chosen and no player has won, then the game is a draw.

Example

  • Player 1 goes first and chooses number \(3\) (from among \(1, 2, 3, 4, 5, 6, 7, 8, 9\)).
  • Player 2 goes next and chooses number \(5\) (from among \(1, 2, 4, 5, 6, 7, 8, 9\)).
  • Player 1 then chooses number \(8\) (from among \(1, 2, 4, 6, 7, 8, 9\)).
  • Player 2 then chooses number \(4\) (from among \(1, 2, 4, 6, 7, 9\)).
  • Player 1 then chooses number \(6\) (from among \(1, 2, 6, 7, 9\)).
  • Player 2 then chooses number \(1\) (from among \(1, 2, 7, 9\)).
  • Player 1 then chooses number \(2\) (from among \(2, 7, 9\)).
  • Player 2 then chooses number \(9\) (from among \(7, 9\)). They win, since they have now collected the three numbers \(9\), \(5\) and \(1\) which add up to \(15\).

Note: A player would not win by choosing just two numbers, such as \(7\) and \(8\), which add up to \(15\). It has to be a collection of three numbers which add up to \(15\).

Instructions

  1. Pick two people to play Game of \(15\).
  2. After the game, cycle through who plays the next game (e.g., winner plays a new challenger, new people play each time).
  3. Continue cycling play for about \(10\) minutes. Everyone should have an opportunity to play.
  4. Determine who is the Champion Game of \(15\) player in your group.
  5. After about \(10\) minutes, discuss strategy for the game, and anything interesting that you’ve noticed about the Game of \(15\). Discuss for about \(5\) minutes, and be prepared to share some thoughts or ideas with the class.