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Taylor and Jessica from Stourport Primary sent this solution to the first part of the problem:

Blue Triangle
Blue Square
Blue Rectangle
Blue Circle

Yellow Circle
Yellow Square
Yellow Rectangle
Yellow Triangle

Red Triangle
Red Rectangle
Red Square
Red Circle

We thought this was correct because it is a very easy way to order these shapes it is also very quick and efficient. We knew that the sequence had to have the same colour or same shape after one another so we ordered them in groups of colour. Which we thought was very clever. After every group of colour it still worked because it was the same shape as the one before for example, Yellow Square, Yellow Circle, Red Circle. After we had finished we checked it through carefully to make sure everything was correct. As we went through we realised that we had made a small mistake but that was soon fixed.

Thank you both. Not many of you tried to find more than one solution, but James from Haytor View Primary sent us two different chains, both of which are different from Taylor and Jessica's:





Oliver, also from Haytor View Primary, sent in two more solutions:





Jed, Jordan, Cameren, Ashley, Charlotte and Lewis, who also go to Haytor View Primary sent in solutions too. Here are their various ideas which are different to those above:



blue triangle
blue square
yellow square
red square
red rectangle
yellow rectangle
blue rectangle
blue circle
yellow circle
yellow triangle
red triangle
red circle


blue triangle
blue oblong
yellow oblong
red oblong
red square
yellow square
blue square
blue circle
yellow circle
yellow triangle
red triangle
red circle

Jack and Charlie from Stourport Primary found another way:

blue triangle
blue circle
blue rectangle
blue square
red square
red rectangle
red triangle,
ellow tringle
yellow rectangle
yellow square
yellow circle
red circle

And here is what was sent by Devansh from Delhi Public School, Vasant Vihar:

To place the same shapes or same colour as per the question we should start first with the Blue triangle then place the Blue Circle then the Yellow Circle, the Yellow Square, the Red Square, the blue Square, the Blue rectangle, the Red rectangle, the Yellow Rectangle, the Yellow Triangle, the Red Triangle and lastly place the Red Circle to complete the sequence.

Do you think we have found all the ways? How will we know?



Lucy, Jodie, Josef, Jack and Jordan from Haytor View looked at the second part and decided that you can't use them all because you run out of pieces to use.



Alistair was able to explain this second part of the problem:

Each piece has to have a pair of the same colour next to it in the line, except for the end and the start. Also each piece has to have a pair of the same shape next to it in the line. To get the longest line, there are exactly ten pieces in the line with two left over. The ten pieces include four shape pairs plus two odd shapes at the ends.

solution

James from Haytor View found another way to do it:

Maybe you can find another way.