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What do you think of this educational game?
It is not easy to think of games for young children that are both educational and strategically interesting. See what you think of this.
The game is for two players, who alternate turns. Start with the numbers 2 through 10. Each player in turn gets to remove a single number and all numbers divisible by it. The winner is the one who takes the last number. The game can be played with pencil and paper.
If I were more ambitious, I would write a computer program for the game, which would allow either two players or one person playing against the computer. I did write a program to find out how to win the game. If you want to try this on your own, with or without a computer, I provide the hint that the game is a win for the first player and there is only one winning first move. I actually guessed the winning move, but used the computer to work out all the different cases.
If you are mathematically inclined and interested in a readable account of how to determine winning moves for games like this, I learned about the theory from this online paper, which is part of a larger book. I used the section on N and P positions, which is how far I have read so far.