Mufflermatics: All Ways Round
There are 24 different ways of placing four colours in a square - or sitting four people round a table. 12 of these can be seen by looking at one side of the scarf. The other 12, which are reflections of the first set, can be seen by turning the scarf over. Folding the scarf in half might lead you to believe that there are only 6 completely different possibilities for the scarf - though this couldn’t happen to the table.
Buy the individual pattern from the link at the top of this page
or in Mufflermatics - a book of mathematical shawls and scarves.