The 100 Game

Players: 2
Ages: 7 and up
Cost: Free!
Math Ideas: Subtraction, deductive reasoning, working backwards
Questions to Ask: 
    What number do you not want to get stuck with?
    How can you avoid getting stuck with 1? With 12?
    Is it better to go first or second? Why?

Sometimes as a teacher, I find myself with a classroom full of kids and nothing to do. Maybe the fall musical ended at 2:55 but school doesn't let out until 3:15. 

Whenever this happens, I pull out the 100 Game. This game can be taught in two minutes but always keeps my students occupied for at least twenty as they battle each other and develop strategies to try to unseat me, the 100 Game World Champion.

How to Play

Write the number 100 at the top of a piece of paper. Two players take turns subtracting whole numbers between 1 and 10. The person who subtracts the number down to zero, loses.

That's it! Like I said, it takes only a minute or two to learn, but the underlying strategy takes quite a bit longer to notice.

When I introduce this game to my students, I like to be extremely arrogant and play up the World Champion angle. I ask for a volunteer to play against me as the official First Loser of the 100 Game. I require that each student win three games against their classmates before they earn the opportunity to lose to me. I even trash talk during the game, which is not usually a part of my typical math class.

All of this is fuel for those couple of students who desperately want to beat me and are willing to go home, sit down with a piece of paper, to finally figure out how to beat me. Every year I have eventually been unseated as World Champion, which is one of the most fun days of the year.

Where's the Math?

The 100 Game is clearly mathematical, but on two levels. 

Most simply, it's a great game for young kids to practice subtraction. A 2nd grader would feel comfortable playing this game, which gives some structure and reason for the repeated subtraction practice. When I play a kid, I make them keep track of both players' moves, which doubles the practice. Each game is the practice equivalent of a classic subtraction worksheet, but your kids won't complain nearly as much.

On another level, this game is about strategy and deductive reasoning. This game, like tic tac toe, is a solved game with a perfect strategy that is discoverable by kids.

At first, kids usually pick random numbers to subtract until they get to around 20. At that point, they really start thinking hard about how to avoid subtracting that last number.

Older kids eventually notice something special about 12. Let's say you choose to subtract 5 to bring the number down to 7. Your opponent subtracts 6, leaving you to subtract the final 1.

So the next round, you get to 12 and subtract 1, leaving the number at 11. Your opponent subtracts 10, forcing you to subtract the final number again!

Hmm, maybe we should ask some questions about that...

Questions to Ask

If your child doesn't notice the significance of 12, I recommend starting a conversation about that number. What is so special about 12 in this game? And is there a way to force your opponent to get 12, so that they end up losing the game? These are the questions that lead my students to eventually dethrone me and take over as the new 100 Game World Champion.

Also, whenever I play a student, I always make sure to ask the same question first: Do you want to go first or second? It seems like a trivial question, but in fact the answer to that question is the key to beating me. 

Hopefully I've piqued your interest about the perfect way to play the 100 Game. I suggest trying it out with your kids or partner and seeing what strategies you come up with. If you think you've cracked the code, send me an email describing it, and I'll reluctantly declare you the Newsletter Champion in next week's edition.