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Binary/Nail Varnish Puzzle – solution

Previously, we posted about Katie’s Binary Nail varnish tutorial video, and how you can use glitter (1) and no glitter (0) to encode binary messages in your nail varnish. We also posted an accompanying puzzle, stated as:

Suppose I want to paint my nails on one hand differently every day for a month – so I need to use all 31 combinations involving glitter. Assuming that a nail painted with plain varnish can have glitter added, but a nail with glitter needs to be nail-varnish-removed before it can become a plain nail again, what order do I apply the different combinations so that you minimise the amount of nail varnish remover I’ll need to use?

Here’s our take on the solution.