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youcubed: Nim Games (3-12)
Mathematical games are often simple to play, but hard to master and Nim Games are no exception.

You only need a handful of beans or coins to play. We have had Nim-7 in our Tasks Page for some time (linked below) but there are many versions of Nim Games you can play and with so many variations, Nim Games can bring entertainment for hours.

Basic idea: Players take turns taking a number of items from the piles available. The player who takes the last item loses.

Rules that can vary:

• Number of objects: Any number of objects can work! For younger children you might want to start with under 10 items, older students might want to extrapolate and think about who would win in a game with more objects than they can count.
• Number of piles: You can start with a single pile or split the items into a few piles (not necessarily evenly split). In their turn, a player can only take items from a single pile.
• Number of items you can take: You can have rules from “you have to take one item in your turn” to “you can take any amount of items from a single pile each turn”. In between, you can have a rule like “you can take 1 or 3 items from a single pile”. Passing on your turn or collecting zero items, however, is not an option.
• Number of players: Nim Games are traditionally played between two players, but how do three or four players taking turns affect the game? Do your strategies change?

You can make your own choices and get really good at the Nim Game of your choosing, or you can feel free to play with combinations of these rules. Which ones make the game most interesting? Are there any combinations that make the game too easy or too hard for one of the players? Can you find a strategy that works every time for the rules of your choosing? What about inverting the game: the player who takes the last item wins?

As you can see, Nim-7, where there is a single pile of 7 objects and players can take one or two in their turn, is a version of the game, but we wanted to share with you all the different ways you can change up the game and make it interesting for everyone!

Problem-Solving
K-6, Middle School, High School, Educator

## Organization

youcubed (Stanford University)

## Type of Resource

Video (Instructional)