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# Fair's Fair

##### Age 11 to 14 ShortChallenge Level

This table shows the possible outcomes when two normal dice (my dice and your dice) are rolled and their scores added together.

You can use the table to see that the probability of getting a sum of $2$ is $\frac1{36}$, the probability of getting a sum of $3$ is $\frac2{36}$ and so on.

My dice
Your dice    1   2   3  4 5 6
1  2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12

Imagine that I change my dice slightly by replacing the 2 with an 8.

Can you choose numbers for the faces of your dice so that the two dice still perform in exactly the same way when thrown as a pair (ie so that the probability of getting a sum of $2$ is still $\frac1{36}$, the probability of getting a sum of $3$ is still $\frac2{36}$, and so on)?

You can find more short problems, arranged by curriculum topic, in our short problems collection.