No. The game is about hats. Not feet. Pay attention.
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There are seven possible combinations
However, if the hats were [r b b], 1 would know her hat instantly, and if the hats were [b r b], 2 would know her hat instantly. That leaves five possible combinations. Also, this means that if she sees one blue and one red, she knows her hat must be red. And, obviously, if she sees two blue hats she knows her hat is red.
There are five possible combinations, and three of them work out to 3’s hat being red. The two tricky ones left over are [r r r] and [r r b].
However, if the hats were [r r b], 2 would see 3’s blue hat and know her own hat can’t possibly be blue, or else 1 would answer red. [R r b] gets thrown out.
In all the cases where the first two answers are don’t know, 3’s hat must be red.
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I’m trying to sort this out as I got this wrong. In your scenario [ r r b], wouldn’t 1 and 2 be in the same situation? 1 would see a red and blue hat, and 2 would see a red and blue hat. From 2’s perspective 1 would only know her hat color if she saw two blue hats. 2 now knows that 1… oh… just got it. Thanks!
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These iterated theory-of-mind puzzles make for an excellent children’s book:
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This is easier to understand if you imagine person B and C, ask A " what color is my hat?"
and A answers to both " I see at least 1 red hat" which is equivalent to "I DNK my hat color"
since the first person A can only know their hat color if they see 2 Blue hats
Then pretend only C asks B “what color is my hat?”
and B answers “I see at least 1 Red hat” which is equivalent to "I DNK my hat color"
since B can know their hat color only if they see a Blue hat on C.
this is true whether or not person A has a red or blue hat on.
B really only needs to look at C’s hat to be able to deduce the color of B’s hat.
since A told them at least one of B and C’s hats is Red.
C can be blind.
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