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The surprising result (to me at least) was that out of 270 valid letter combinations, 105 can be reversed. The odd number is easy to explain: letter pairs like MM => MM can add a single flag instead of a pair of two flags, but the fact that almost two out of every five flags are reversible feels pretty high to me.

but the fact that almost two out of every five flags are reversible feels pretty high to me.

I think some letter-frequency analysis can probably explain it. Given the fact that certain letters are less likely both as the first slot and second (e.g., there are only 4 country codes that start with J, and 3 that end with J), the letters that can be used as both first and second characters are over-represented.

It's the same as how far more English language words can be reversed to make other valid words than you would expect if the letters were equally-frequent and arbitrarily arranged.

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