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Domino Square

Stage: 2 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

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