My guess in the spoiler.
think the answer is b, a, c never knows
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My guess is C first. She can see the black hat in front of her, so knows she has a white hat (since she knows there’s only one black hat). C says “white,” so B now knows there are two white hats on other people. B says “black,” then A says “white.”
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two black hats or two white hats but they don’t know which.
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I think @Daveb is right.
To begin with nobody can tell what hat they have on, so nobody says anything. THIS IS NEW INFORMATION.
B then shouts out that they have a black hat on, because If C can’t tell what kind of hat they have on, then they must have the opposite colour to A’s hat, which they can see.
Then, Once that has happened, A can work out, following the same logic, that they have to have the opposite colour of hat to B, So they now shout out their hat colour.
C can see both of these hats, so they get no new information from these people shouting out their hat colours, and remain in the dark about their own hat.
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C can’t know because she sees one of each color.
B only sees one color in front of her, so if she waits a bit and C doesn’t say anything (and she has a reasonable expectation that C isn’t dumb), then she can announce her hat as being the opposite color to the one in front of her.
A doesn’t know if C sees white on her and black on B, or vice versa, so she can’t know until B announces her color, at which point A can announce the opposite color.
edited to add: I see that Purplecat has already spelled it out in much greater detail!
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I missed the vice versa!
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First read through missed it as well.
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If 1=white and 0=black, it seems to me the solution rests on whether the puzzle can be interpreted as:
-
Only two possibilities: Either 101 or 010 (i.e., middle is always different)
-
Three possibilities: 101, 010, or 001 (i.e., only one black hat)
OR
- Six possibilities: 011, 101, 110, 100, 010, or 001 (two white hats or two black hats).
I missed the “vice versa” so assumed interpretation #2. So is the real puzzle #1 or #3? (If #1 then it’s obvious that B will guess first.)
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3 is a’ s perspective b knows if a is 0 or 1 but not if b and c are 0 or 1 and c knows a and bs values but not their own unless b==c at which point c can infer their own value. So the puzzle is how do the answers or lack of answers fill in the other players lack of knowledge.
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It depends on the interpretation of “like the one shown above.” Assuming that its either w-b-w or vice-versa b-w-b, alternating “like the one shown above,” then B and G can tell at a glance.
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There a four hats for three people 2 white and 2 black for each person someone they can’t see flips a coin to decide which hat they get. The first person stands there and has a hat put on his head the second stands behind them coin flips again and so on. Then the puzzle starts.
Answer in magazine
New puzzle next to it.
I got 7 moves. Don’t know if theres a better score or not.
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3 moves:
1: find the person who put them back out of order
2: beat them senseless
3: when they come to, make them fix it
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Nice. You win.
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Does rotation count as sliding? If 2 books are next to each other, does moving them together count as a 1 move or 2?
If yes to both, then A. 2 between 1 and 4, B. 3 between 1 and 4, C. 9 and 8 between 10 and 7 and rotate 180Ëš on an axis perpendicular to the row.
If no to the 1st question, are these magnetized books on a curved shelf that would leave them inverted if slid far enough?