Sum 15

Description

“Sum 15” is a simple, engaging, educational game. It was created to help both Middle and High School students develop their skills in mathematics as well as logical thinking in a light and fun way.

Rules of the game

1. It begins with the possibility to choose between 9 numbers: 1, 2, 3, 4, 5, 6, 7, 8 and 9. The players must take turns playing until the end of the game.
   
2. At each player’s turn, he chooses one of the available numbers. After a number is selected, it is no longer available.
   
3. A new round begins when both players have made their choices.
   
4. The goal of the game is to get 15 out of the sum of 3 chosen numbers. When one of the players gets it, the game is over, and he is declared the winner.
   
5. In case none of the players wins the game and there are no more available numbers, the game ends with a tie.

Example of winning games

Example 1
Player A chooses 1, 4, 8, 3.
Player B chooses 2, 9, 7.
Player A wins with the triple: 3, 4, 8.

Example 2
Player A chooses 5, 6, 8.
Player B chooses 9, 4, 2.
Player B wins with the triple: 2, 4, 9.

Strategies

Different strategies can be used to win, for instance, we can start by choosing the number 5, since it is the number with the most options to have a sum equal to 15: (1,5,9);(2,5,8);(3,5,7);(4,5,6).

The second player is limited to reactive responses since he starts with a disadvantage.

Interesting surprise

Until now, this game may seem more complicated than it is, however, we are playing a very common game, it just has a disguise on. It is very likely that everyone you know has played it at least once in their life. ‘Sum 15’ is just a different take on Tic Tac Toe.

To explain it better, let’s look at ‘Sum 15’ in an abstract way. Considering the following matrix:

2	9	4
7	5	3
6	1	8

Notice that the numbers in the matrix are the same as the numbers available during the game. Also, if we sum the numbers diagonally, vertically or horizontally we get 15 as a result. So, for someone to win, they must get a complete line, column or diagonal.

Let’s see an example so that the similarities between the two games become clearer.

Let’s consider that player A begins the match and chooses number 5, and player B chooses number 4, so after the first round we have:

2	9	4
7	5	3
6	1	8

If we were playing Tic Tac Toe this is what it would look like:

		O
	X

In the second round, player A chooses number 8 and player B chooses number 9, so we have:

2	9	4
7	5	3
6	1	8

And the equivalent Tic Tac Toe board would be:

	O	O
	X
		X

Finally, player A chooses number 2 and wins the game:

2	9	4
7	5	3
6	1	8

If it were Tic Tac Toe:

X	O	O
	X
		X