Otro Nim

	ANOTHER GAME OF NIM
	Section

5. ANOTHER GAME OF NIM

Here you can check whether you have understood the procedure to win at Nim.

We now have eight groups. The number of objects in each group is 1, 3, 5, 7, 9, 11, 13 and 15 and the rules are the same as those stated at the beginning.

1) You can only take objects away from one group at a time.

2) You can take away as many objects as you want.

3) The winner is the one who takes away the last object

However, another version of Nim can be played in the same window where the third rule states:

3') The player who takes away the last object loses.

I will explain how to play this other version at the end.

When playing with so many groups and quantities in each group it is useful to have the following table to refer to. It will help you know how many objects you should take away:

Base

100

101

110

111

1000

1001

1010

1011

1100

1101

1110

1111

Click on the init and animate buttons to play. If you don't want to see the previous moves click on clear.

Esta unidad interactiva requiere la máquina virtual de Java J2RE.

You can use this window to play with other quantities of objects or to play the other version of Nim.

In order to do so click on the right-hand button of the mouse when it is on the window. Click on the init button (using the left-hand button of the mouse) in the window which appears and use the arrows to choose your values. In the box last object loses?, 0 means no and 1 means yes. Afterwards, click on the animate button and then on close.

Use the buttons in the window for GROUP and TAKE AWAY to play.

Click on the clear button to get rid of previous moves.

EXERCISE 6:

What is the strategy we need to use to win when "the one who takes away the last object loses"? Try playing with few groups and you will see that the strategy is the same except for the very end.

	Juan Simón Santamaría

	Spanish Ministry of Education. Year 2002

Except where otherwise noted, this work is licensed under a Creative Common License