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Khoth comments on Open Thread March 31 - April 7 2014 - Less Wrong Discussion
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There's no need for an enumeration of all the sequences, bayl na rahzrengvba bs gur rdhvinyrapr pynff gung gur cevfbaref frr gung gurl'er va jura gur ungf ner cynprq. Naq Bfpne_Phaavatunz'f fbyhgvba qbrfa'g arrq rira gung -- gur rdhvinyrapr pynffrf pna or nal genafsvavgr fvmr jungrire.
I'm now wondering whether for the case of two colours, there is a computable algorithm. A prisoner would apply the algorithm by feeding it an infinite tape listing all the colours of the hats, with a blank for his own, and the algorithm would in a finite time say what guess to make.
It seems unlikely. In a finite time it's impossible to get any idea whatsoever what equivalence class they're in, so the solution, if there is one, would need to be very different.