All 21 squares start in the same way. Each subsequent square is the same as the one before with an extra band. I used four colours but the design could be made in any number of colours.

The squares are made individually then joined together.

There is a minor conflict between the mathematics of the design and the numbers needed to make squares lie flat. The squares do not lie flat automatically but can be blocked flat.

We do not recommend using this design as a wall-hanging as any undulations may reappear.

CROCHET INFORMATION

21 squares worked using the same stitch throughout.

The construction of the squares is a little unconventional and is explained in detail in the instructions.

For many years mathematicians had tried to find the smallest number of different squares needed to make a larger square. In 1939 Roland Sprague did it using 55 squares. Nearly 40 years later, A.J.W.Duijvestjin found the solution shown here. It uses 21 different squares. No one has yet found a solution with fewer squares.

In 1997 we made Square Deal, which was our first afghan based on this design.

In 2011 the afghan was mentioned in a book called Crafting By Concepts. This inspired us to revisit the design and create the crochet version. It is easy to identify the 21 squares as the number of rounds of crochet in each square corresponds to the unit size given in the diagram. Each square starts in the same way with the next size up having an extra band in a new colour.

The crochet squares accurately represent the relative sizes of the squares. This means that they do not conform to any of the conventional ways of making squares. There is conflict between the two sets of calculations. We could not find any other kind of square that would work exactly without making an afghan that was much too big for practical use.