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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)?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...