For the advanced variations a calculator may be used. The challenger always has the choice of going first or second. Students alternate subtracting one or two from the number they receive . The winner is the player who adds or subtracts to get to zero. The variations suggested below can be modified in any way to create new variations.
Students are fond of creating and playing their own variations.
It does not take long for students to master NIM - 7. A resignation is considered a noble way to end a game if the outcome seems determined. Masters of NIM become the students who can determine all the critical numbers. Also, it is important to determine the advantage of going first or second. Have students color the critical numbers to identify them.