# Squaring the square, in glass

Here is my latest stained glass effort, seen on a snowy day.

It is a 'square of squares', where all the constituent squares are of different sizes. Here are the dimensions -

It is copied from the logo of the Trinity Mathematical Society, who point out that it is the *unique smallest simple squared square (smallest in that it uses the fewest squares, and simple in that no proper subset of the squares of size at least 2 forms a rectangle).* It was proved to be the smallest such square by Duijvestijn in 1978, but this was by exhaustive computer search, which seems a bit like cheating.

There is a fine Wikipedia site which contains more than you ever wish to know about squaring-the-square.

## Challenge

I wanted to only use 4 colours without any square touching another of the same colour, and of course I knew this is possible due to the 4-colour theorem. But I wanted the four large outer squares to be 'white' (in order to increase the Mondrian appeal). It took some effort and trial-and-error to find a 4-colouring with this property. Are there others?

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## Comments

Perhaps

Fri, 01/02/2013 - 4:31pm

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## More solutions

Perhaps

Fri, 01/02/2013 - 4:36pm

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## 6 more

whuber

Wed, 06/02/2013 - 4:29pm

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## All solutions

david

Wed, 06/02/2013 - 5:19pm

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## wonderful!

A beautiful array. It is tempting to try a vast stained glass window featuring all of these!

Perhaps

Wed, 06/02/2013 - 6:50pm

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## Field 11 and 19 are the same

whuber

Wed, 06/02/2013 - 9:20pm

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## Correction

jhodsdon

Thu, 26/09/2013 - 4:31pm

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## Challenge