Who got Fifteen – A Math Addition 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.

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.