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Challenge 443: Plaiting hair

The classic problem of trisecting some hair!

From Noa, one of my Y13 students:

"When I plait my hair, I need to split it into six equal sections. First, I split my hair in half down the middle. This is easy, because I am able to grab equal amounts of hair in each hand. Next I need to split each half into three equal pieces. This is much more difficult! Is there a mathematical way I can use to separate my hair roughly into thirds?"

To clarify, two operations are possible: (a) Noa can divide a section of hair into two equal subsections; (b) Noa can combine two sections of hair into one super-section.