Latin Squares and Euler Squares

Yesterday in 4G, as a five minute thing at the start of the maths lesson, the challenge was to make Latin squares, where each colour appears only once in each row and column of a square:

Mr Gregg tweeted an image of this and got a reply that took it further:

@Simon_Gregg good one! You can propose a latin square with no colour repetition on the diagonals
— Daniel Ruiz Aguilera (@druizaguilera) June 26, 2014

So... diagonals...
We used a Word document (switching the gridlines - 2cm - on, to snap to grid) as there aren't enough plastic squares for everyone to have a go!

Ryan was the first one to get it!

Well done Ryan! After that, lots of others found a way.

Mr Gregg had had another tweet:

@tocamates @druizaguilera @Simon_Gregg we're talking diagonal squares here! Actually you can go MUCH further: http://t.co/jpK4ckkIAL
— theoremoftheday (@theoremoftheday) June 26, 2014

So, now for something much harder.... Euler squares! (We've met Mr Euler before!)

Mr Gregg had made a Word document for this too. This time there are shapes and colours, and both have to be organised!

Mr Gregg said we wouldn't try for very long because it looked very hard! But, just as he said, "Right, that's enough," Rozenn shouted out, "I've done it!"

And she had - well done Rozenn!

 Here it is, recreated in plastic squares:

A big thank you to all the people on twitter who helped us!

PS

Mr Euler said it was not possible to make this kind of square if its size is 2, 6, 10, 14...

He was right about 2 and 6, but in 1960 it was discovered it is possible with 10 and all the others: