Purple parity at a party: The Wknd Puzzle by Dilip D’Souza

Surabhi got tired of playing the same games at her birthday parties. This is the strategy, because her answer is the “parity” of the number of purple hats — whether it’s even or odd — and this clue is passed on. Let’s say the first to be asked shouts “purple”, meaning she sees an odd number of purples. If it’s even, she knows her hat must be purple, because the guest behind saw an odd number of purples. After the first shout tells her the parity of purples to begin with — odd, in this case — she switches that parity with every shout of “purple”, ignoring the shouts of “orange”.