Tue Aug 30, 2016 4:48 am by tartle |
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A warden takes prisoner A into a room containing a chessboard, on each square of which is a coin randomly showing heads or tails. He then indicates a random square on that board. Prisoner A is given the chance to flip one coin (or none), then taken from the room, after which prisoner B is taken into the room and must say which square the warden indicated. The two prisoners may strategize beforehand, but may not communicate during the trial (except with the single coin flip). What should be their strategy? |
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Sun Jan 08, 2017 3:23 am by anon |
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Does A turn the coin (A chooses) over or flip it by throwing it (random)? |
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Sun Mar 26, 2017 9:48 pm by batze |
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Solution for a 2-square chessboard:
HH -> HH / TH
HT -> HH / HT
TH -> HH / TH
TT -> TT / HT
The 2 cases are:
1. both the same
2. different
And now a solution for a 3-square chessboard:
HHH -> HHH / HTH / HHT
HHT -> HHH / THT / HHT
HTH -> HHH / HTH / TTH
HTT -> TTT / HTH / HHT
THH -> HHH / THT / THH
THT -> TTT / THT / THH
TTH -> TTT / HTH / THH
TTT -> TTT / THT / TTH
Here the 3 cases are:
1. all the same
2. single outlier in the middle
3. single outlier at the border
This should be extendable to 64 squares, but the pattern rules will become more and more complicated. |
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