We tried a dice puzzle today set a while back by Matt Parker.
You only have the tool above – three dice inside a cube.
But you want to play a game that requires throwing a single dice and then a game that requires throwing two dice and adding their score together. Is there a way that you can use the sum of these three dice to simulate both of these scenarios?
Task 1
First work out the distribution of numbers you can score with three dice
| Sum | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| Number of ways |
Can you map this in a nice way to the distribution for 1 dice?
| Sum | 1 | 2 | 3 | 4 | 5 | 6 |
| Number of ways |
Task 2
How about for 2 dice?
| Sum | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| Number of ways |
Might not be able to do it using (only) the sum …
Printable worksheet here.
Succinct solution here or watch the full brilliant video by Matt.