perplexus.info :: Games : A game of 15

A game of 15 (Posted on 2002-05-10)

Two players play this game. Numbers from 1 to 9 are layed out in a row. Players take turns putting a coin on one of the numbers that does not yet have a coin on it. Player one puts his coins head-up, and player two -- tails-up.

The winner of this game is the first person to have their coins on three numbers that add up to 15. (For example if a player has coins on 1, 6 and 9, they can win the game by putting a coin on either 8 or 5.)

Is there a strategy for playing this game? Is there a sure-fire way of winning?

Submitted by levik

Rating: 4.1333 (15 votes)

Solution: (Hide)

Consider the following table:
6 1 8 7 5 3 2 9 4
This is a "magic" square, in which the sum of all columns, rows and diagonals is 15. Incidentally these 8 combinations are all the ways to make 15 out of 3 different numbers in the range of 1 - 9.
Taking turns putting a coin on these numbers is equivalent to a game of tic-tac-toe. A person who has the magic square above to refer to is at a significant advantage, and though as with regular tic-tac-toe, victory is never assured, they will always be able to avoid defeat.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-08-20 21:57:31
cool	RandyOrton	2004-11-30 19:30:55
fun	calla tah-n	2003-05-18 21:37:48
What a great game for the classroom	cges	2002-12-12 06:05:44
Strategy	TomM	2002-05-10 18:21:34

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