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Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

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4 Dom

Use these four dominoes to make a square that has the same number of dots on each side.

Domino Square

Stage: 2, 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Andrew and Michael from Old Earth Primary, and Sam, Harry, Molly and Callum from St Nicolas C of E Junior School, Newbury started this challenge in the same way. Here is what Sam and Harry said:

Sam and I, Harry, counted all the dots on the double-3 down dominoes, so we got 30. But we needed 8 dots on each row and 8 x 4 = 32.
So we knew we had to put 2 dots in the corners because the dots in the corners count double because they are in two rows.

Andy and Michael expanded a bit on this:

All the corners must add up to 2, which is either 0, 0, 0, 2 or 0, 0, 1, 1.

In other words, the dots in the four corners must make a total of 2 dots. The only ways to have a total of 2 dots is by having one corner with 2 dots and the others all blank, or two corners blank and two with one dot.

Sam and Harry found this solution which had 2 dots in one corner and the other corners blank:

Ellie and Kerry from Stoke Mandeville Combined School also sent a picture of the same solution. Thank you! Andrew and Michael found a different solution, using 2 dots in one corner:

Rather than draw dominoes, they have chosen to write digits to represent the spots, which might be a bit quicker!

Livvy and Connor from Cutthorpe got out their dominoes and experimented. They also found a solution with just 2 dots in one corner:

Abbas, Alfin, Yasemin and Godwin from Archbishop Lanfranc also found the solution above. Lucy from Middlefield School said:

I cut out all the dominoes on the sheet. I then experimented by sorting out one side, then the next and so on until I did it.

Lucy discovered another way to arrange the dominoes with 2 dots in one of the corners:

Tom and Ted from Ysgol Abergynolwyn thought that blanks worked best in the corners and they found yet another way using a 2 in one corner:

Are there any more ways to arrange the dominoes with a 2 in one corner and the other corners blank? Let us know if you find any.

Molly and Callum from St Nicolas C of E Junior School, Newbury found a solution which has two blanks and two ones in the corners:

We also had three other solutions sent in which had two blanks and two ones in the corners. Here is Nick's (who goes to the English College in Dubai):

seventh solution

Rebecca and Amy from Sawtry CC sent this one, saying that they used trial and error to work this out, starting with the double 3 on the top line and working through:

eighth solution

And Rachael from Old Earth Primary sent this:

ninth solution

Jay from Carmyle Primary in Glasgow sent in the following one later on and I'm pleased to say found one that is different.


So many solutions! But are there any others with two ones and two blanks in the corners? Do let us know.