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Fun for math nerds: How many ways are there to lace a shoe?

This is the most interesting, refreshing sentence I’ve seen in the newspaper in weeks:

More precisely, this condition says the shoelace is not allowed to pass in a straight line through three consecutive eyelets on the same flap; otherwise, the middle of the three eyelets does not actively help close the shoe.

During a road trip a few years back, I wrote a PERL script to calculate how many unique combinations a burglar would have to try to brute-force the lockbox hanging on my back door (put there by a general contractor during a bathroom remodel). The answer was 715, fewer than what you’d expect from a 4-digit key (which in a more-secure design would yield 10^4 or 10,000 combinations).

Alas, my analysis did not get published in Nature, perhaps because the editors realized that the easiest way to brute-force a lockbox is with a hammer. And it would take a lot fewer than 715 blows.