Nim and Ximo Games

When I was teaching high school math I often used the first two versions of Nim that are found in this flipchart. At the start of the school year I'd use them for filler if we had five or ten minutes at the end of a class. Some students loved them and would challenge me to games throughout the year. The simple tools in this flipchart make it quick to set up and easy to play.

The third version of the game is one that I created called Ximo. It hasn't been universally loved, but it is exactly what I wanted it to be--a variation that makes each game a new challenge.

Playing "One Brain Against the Class"
This could be a fun, ongoing way to play each day in an advanced class if you have Expressions for your students. It is suggested that the individual and the class each make one move a day as part of any other warm-up for the daily lesson.

1. On the game setup, label the rows of the setup r1, r2 and r3. (If you're playing the Tactix game, label rows and columns.)
2. The player who is taking on the class (which should probably be the teacher the first time) takes a turn as usual.
3. For the class' turn, start a Text Entry question using Express Poll.
4. Students can enter their move suggestion on the Expressions. No discussion allowed! For example, with the 3-row version of Nim if they wanted to remove two disks from row 2, they would enter r2,2. It's important that they use strict conventions on entering moves. See the note below for trying this with Tactix.
5. After the vote, view the results. Remove the dots that were suggested by the most students. For example, if r3,4 was the number one response, take 4 dots from the third row. Again, students need to follow the exact format on entry so that the results are counted correctly.
6. If there's a tie for the number one move suggestion you can either randomly select one or have the class vote on the tied moves using Express Poll again.
7. Play until the individual player or the class wins.

Tactix is more complex for entering the moves. Label the rows and columns. Players will indicate which dots are removed by row or column number, then a number range for the dot(s) removed. To take the first three dots from column 1, for example, they would enter c1,1,3 (first column, dot 1 to dot3). r4,3,4 would take dots 3 and 4 from row 4 and c3,5 would be used to take just dot 5 from column 3.

Be sure to check out the entry at Wikipedia if you are unfamiliar with the game. Several other sites can be easily found that allow you to play online.

This one at Math.com has been entertaining.