My guess in the spoiler.
think the answer is b, a, c never knows
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.”
two black hats or two white hats but they don’t know which.
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.
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!
I missed the vice versa!
First read through missed it as well.
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)
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.)
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.
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.
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.
1: find the person who put them back out of order
2: beat them senseless
3: when they come to, make them fix it
Nice. You win.
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 180˚ 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?