Who got Fifteen – A Math Addition Game

Who got fifteen - math strategy game

Who got Fifteen is a simple math game of addition which you can play anywhere anytime, while waiting at a restaurant or while on the go. All you need for this game is a paper and a pencil. Though this game only has simple additions to do but it can keep you captivated for long.


To play this game, each player takes turn to choose a whole number between 1 to 9. (You can mark your chosen number with an ‘X’ and another player can mark their chosen number with an ‘O’ to keep a track of the chosen numbers respectively). Only rule is that each number can only be chosen once. The player who first selects 3 numbers who add up to 15 is the Winner.

If each player has chosen 3 numbers and neither player has a total of 15, then keep playing until one of the player has any 3 digits which total to 15. If all the numbers are chosen and none of the players has any 3 digits adding up to 15, then it’s a draw.

Can you figure out what can be the strategy here.

  • Does it matter who start the game first ? Does it increase the probability to win ?
  • Can you spot the pattern here ?
  • Can you find the similarities between this game and any other games you know.

Let’s give it a try.

So, what is the strategy here ?

There are eight subsets of three numbers which when added gives 15. These subsets are [1,5,9],  [2,5,8], [3,5,7], [4,5,6], [1,6,8],  [2,4,9], [2,7,6] and [3,4,8]. These subsets can be placed down as a 3 X 3 magic square.

Magic square where sum of each side is 15

The three rows,  the three columns and the two diagonals of the magic square sum up to 15 each. So, basically, you are playing Tic-Tac-Toe on the magic square. And it doesn’t matter, which player starts first.

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