how did john know ? solution.

if peter saw that james and john both had white hats on their heads, he would say, “i know the color of my hat — black.”  but because he couldn’t know the color of his hat, seeing james’ and john’s hats, it must not be both white.

if james saw that john had a white hat on, he would say, “i know the color of my hat — black.”  james already knew, from what peter said, that his and john’s hats cannot be both white; so if john’s hat was white, james knew that his was black.

it’s as simple as that.

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