how did john know ?

i have five hats in my bag which you cannot see — two white and three black,” andrew said, “and i will put a hat on each of your heads.”

peter, james, and john stood on a single file, one in front of the other — peter at the rear, james in the middle, and john in front.  andrew put a hat on each of their heads and said, “can you tell me the color of the hat i put on your head without looking at it?”

peter (who was at the rear) said, “i can see the color of james’ and john’s hats, but i don’t know the color of my hat!”

james (in the middle) said, “i can see the color of john’s hat, but i don’t know the color of my hat!”

john (in front) said, “hmm… i cannot see the color of peter’s and james’ hats, but i know the color of my hat!”

how did john — without looking — know?  what is the color of john’s hat?

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