# Square Puzzle

The challenge is to turn a square of fabric into a jacket without cutting off any pieces or adding anything on. It can be for a child, adult, or, in this particular case, Barbie.

You are allowed to make cuts into the fabric, and join it back together as you wish. Nothing can be added or removed.

This is the way clothes would have been made from animal skins to use the maximum amount of skin with the minimum amount of skill and effort.

Does the problem become easier if some cuts are made for you?

Fold in the sides.
Fold down the top.

The underneath edges of the sleeves can be stitched, or laced, together and the rest of the top can be joined to the front panels, to give a recognisable jacket shape.

Somewhere we have a large-person-size version of this jacket made from heavy navy woollen fabric. The slits are created with shiny metal open-ended zips which can put it back together as a square or a jacket. Unfortunately we haven’t been able to find it to photograph. Neither do we have a video of Ben zipping himself into it during a talk at a maths conference some years ago.

Barbie size will have to suffice. The advantage of Barbie is that her neck is so narrow you don’t need to make allowances for it. A human garment would need to have some extra cuts at the neck to let it wrap round.

With knitting, and crochet, you can add the slits as you go. The square can then be folded to the correct shape. This one is fastened with buttons.

Barbie’s pink and grey outfit consists entirely of squares. Her trousers are four identical squares – one for the back, one for the front, and one for each leg. Her top is made from two squares, joined at the sides and shoulders. Her hat is a square folded in half.

The square could be made from four smaller squares. This allows for some extra patterning. These squares are knitted on the diagonal, starting at a point.

The red lines show the positions of the slits, where the squares should not be joined together in the flat view.

The front view and back view create very different effects.

The black and white trousers are made from rectangles knitted on the diagonal. A rectangle is merely an elongated square.

Increase at the end of every row in the same way as for a diagonal square until you reach the width you want (red line). Continue to increase at one edge and decrease at the other. It doesnâ€™t look much like a rectangle until you stand it up.

When the long side of the shape is the length you want (blue line) start decreasing at both edges. This shaping will always give you 90 degree angles so could be used for any rectangle, such as a for a scarf.

Barbie’s brown outfit is very similar to the others except that it is crochet.

The fluffy outfit uses the same pattern knitted longer and with extended sleeves. The dress is a simple square, seamed at the back.

All outfits, plus a mini-tutorial about squares, are included in the same pattern.