Question: 12. Suppose we are playing the 31-hat game, and there are 11 red hats, those on players from 10 to 20 [inclusive]. Let's call this

12. Suppose we are playing the 31-hat game, and there are 11 red hats, those on players from 10 to 20 [inclusive]. Let's call this state x. (a) Is the state winning or losing? (b) How does each player vote? Provide an explanation. (c) Among the 31 neighbours of state x, how many are B states? (d) Now consider all the states that differ from x in exactly two slots. We might describe these as \"neighbours of neighbours ofx.\" How many ofthese are B states

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