Puzzle thread? Puzzle thread.

[Xei]

Great job Dianeva, I did basically the same thing. Spoiler for Solution to Sixty Sombreros: The very first guy counts the number of white hats of the 59 prisoners in front of him. If it's even, he says "white", if it's odd, he says "black". The code could be the other way round, it doesn't matter - point is, he communicates to the other 59 prisoners whether the number of white hats is even or odd. There's a 50% chance that the codeword happens to coincide with the colour of his hat and he isn't shot. The rest can then easily ensure their survival. The first guy of the remaining 59 can easily work out the colour of his hat based on the number of white hats he sees in front of him, and whether the total number of white hats for all 59 men is even or odd. The second guy can also easily work out the colour of his hat based on the number of white hats in front of him, the colour of the first guy's hat, and whether the total number of white hats is even or odd. And so on. I got this one really quickly and I have no idea how. Can you remember anything about your thought processes prior to the insight, Di? Interesting that you went for a smoke. The guy told me the puzzle at the pub and I think I went to pee. I recall realising how to do the prisoner one in the same circumstance.