NUMBER SYSTEMS
Maths Workshop
 
4. HOW CAN WE WIN AT NIM?

The following window will help you to win at Nim. Follow these steps to find out:

1.- Write the number of objects that there are in each group in base 2.

2.- Write the numbers, one under another like a sum.

3.- Add each column up in base 10.

4.- In order to win, each time you have to take objects away you have to make sure that the sum of each column is equal to an even number or 0.

The objects in each group, including those which you take away, are shown in the middle of the window in base 2 and in base 10. If you are playing correctly the sum of the columns appears in green. If not, the column which is not correct will be highlighted in pink.

EXERCISE 5:

a) Choose five different quantities for each group so that whoever has to move next will lose.

b) Imagine the following situation:

 

Nº of objects in base 10

Nº of objects in base 2

GROUP 1

1

1

GROUP 2

1

1

GROUP 3

3

11

GROUP 4

1

1

GROUP 5

5

101

How many objects do we need to take away and from which group to be in the winning position?

c) Nim can be played with as many groups as you want and with as many objects as you want in each group. Find all the possible quantities (less than 8 altogether) for a total of three groups so that the next player who moves will lose. For example (1, 2, 3)

d) Why does the strategy outlined at the beginning allow you to win?

  Índice de unidad   Cambios de base   Juego grande  
           
  Juan Simón Santamaría
 
Spanish Ministry of Education. Year 2002
 
 

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