This is a game for you to play, either on your own or with the help of a friend. You need eleven counters and two ordinary 1-6 dice. Draw out a board like this:

Eleven rows of four squares, directly underneath one another. Left hand square in each row coloured purple, right hand square numbered from 2 (top row) to 12 (bottom row).

(You may find that squared paper is useful!)

Place one of the eleven counters on each of the squares numbered 2 to 12.

Throw the dice and add together the two numbers shown. Move the counter on that square one box to the left. Now throw the dice again and repeat this, each time moving the counter on that "row"one box to the left.

Which counter reaches the purple box first?

Is this what you would expect?

Play a few more times and make a note of which counter reaches the end of its row first.

Can you explain why you get these results?