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'One Big Triangle' printed from http://nrich.maths.org/

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Well done to two schools that sent in a picture of their solution, firstly class 4M at St. James' School in England and from Yunsil at Ballybay Elementary School in The Republic of Ireland. Congratulations and thanks for the picture.

Catherine sent us her solution. Is it the same as yours?

Nicole from Mercy College told us:
To work this out I just did trial and error and kept on working out different ways until finally after five minutes I got the answer.

I like to think of 'trial and error' as 'trial and improvement'! This is certainly a good strategy for this problem.  Their completed triangle was the same as the very first one above.

Pupils at St Michael's Kirkham wrote:
We looked at the numbers on the triangles and found the number bonds to $10$. We had to decide which triangle to start with so the rest of them would fit in. We used the colours to help us as well.

Ryan, Josh and Jake from Marpool Primary School also spotted that the colours were useful:
We have found a solution for One Big Triangle.
Each colour must match when putting number bonds to ten together.
You first have to find the triangle that has the numbers $8$, $3$ and $2$ and put it in the bottom left hand corner because the number bonds will not work in any other way. Then put the triangle with $9$, $9$ and $4$ and put it in the bottom right corner. Then it should be easier to work it out from then on.

Cerys and Rachael from Ysgol Bryncrug, Tywyn, Gwynedd sent a photo of their completed triangle:

Using printed cards makes the problem a bit harder as each triangle can be rotated too.

Jack from Birchwood, Suffolk also had a good strategy:
The easiest way was to start from the bottom and work towards the top.
I realised that certain numbers couldn't be paired to make $10$ so I put them at the bottom so they didn't have to link up with anything.

Sion gave us a very detailed explanation, which is very clear:
The first thing that you have to look for is the triangle that can only go in a limited amount of spaces or where the there are only a few numbers that add up to ten with it. In this case it is the triangle with the two nines and a four. I would put this in a corner.
After you have found this you have to look for the triangles that match e.g. the two fives. They both have a one but only one of them has a one that could connect to a nine if the nine was in a corner.
After you have solved one piece, look for the pieces that can add up to the remaining faces of the other triangles. The triangle with a seven in the red part and the triangle with the three in the red must go on the bottom because there aren't any of the other number to make ten with.
There are now four empty spaces two for the pair with the two and eight in the red areas and two for the pair with the nine and one in it. Look where they could connect, the blue areas on the triangles with one and eight. Match them up and their respective partners.

Finally, Jack, Kyle, Louis, George, and Mr. Phillips from Hennock School sent this PowerPoint file which explains how to complete the triangle.