Arthur from Cambridge (12 years), has sent what he found out about adding two dice and subtracting another. He does a really good job of clearly explaining what he did. He says........

First I worked out all the totals that you can get from adding two dice (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12). Then I started doing the take-aways for the third one but started getting in a muddle, so I made a table. Down the side I wrote all the totals for the two dice. Across the top I put the numbers from the dice to take-away. Then I filled in all the answers.

There's a pattern of all the same answers in the diagonals. If you look sloping the other way there's a pattern on both sides of the zeros. There's odd and even numbers in a line.

To find out which answer came up the most I counted. I wrote a list of all the answers and underneath them I wrote how many time you get that answer.

There's another pattern. The numbers from 1 to 6 all can happen 6 times. I wondered if this is because they are the numbers on the dice. Taking away one dice sort of cancels out one of the other dice so there's just one dice left. That seems to make sense but I'm not sure.