## Introduction: How to Play and Win a NIM-game

A NIM-game is a tactical game.

It is played by two players who take turns and pick one or more objects from two or more rows.

The intention is to let the other player pick the last object.

The objects could be anything, from stones to coins.

I am going to teach you how you can play and win a NIM-game.

There is a version of a NIM-game on the internet called Pearls (http://www.transience.com.au/pearl3.html).

It is a good way to practice it.

## Step 1: How to Play a NIM-game

I am going to teach you how to play a NIM-game using the site http://www.transience.com.au/pearl3.html.

This are the rules.

- in each game the pearls are grouped into horizontal rows

- in alternating turns you remove pearls from the game

- in a game you can remove as many pearls you want from any row you want

- the player who leaves the last pearl to the other player to take is the winner

(the pearls could be anything you want, but they are used in the internet game so I use them as a example)

## Step 2: How to Win a NIM-game

When you try winning, you probably won't accomplish, because there is a trick to win every game.**1. When you want to win a game you first have to count the pearls in each row**

for example: row 1= 6 pearls, row 2= 8 pearls**2. Convert the number of pearls into a binary number**

for example: row 1= 0110, row 2= 1000

(when you don't know how to count with binary numbers, here is a tool to convert from decimal to binary. http://acc6.its.brooklyn.cuny.edu/~gurwitz/core5/nav2tool.html)**3. Add the two binary numbers**

for example:

0110

1000 +

1110**4. Change one row so the answer is 0000**

for example:

0110

0110 +

0000

I changed the second row to 4 so the answer is 0000**5. Repeat step 1 up to 4 until you won the game**

when you do this every time you will always win

When you have any questions, please discribe.

## 2 Comments

2 years ago on Step 2

A variant: if objects are taken from the middle of a group, it results in two or more groups. e.g., consider a group of seven: ABCEDFGH; suppose I remove three objects - say, BCF (a move which complies with all rules). The residual is: A, ED, GH - three groups. It is an interesting way to confuse a player who has achieved a winning position, and sometimes can produce an alternative winning position.

7 years ago on Introduction

I think it should be specified that when adding, don't carry.