To resucitate a thread which is no longer breathing:
eytanz wrote:
There are four boxes, labeled....
I can't find a really elegant or convincing way to do this, but here's my attempt. Let's call the boxes P/N, N/D, D/Q, only Q respectively.
Label the boxes 1 through 4, otherwise you'll forget what you're doing. Draw one coin from each of the boxes. Since the one box always gives Q, there are 2^3 combinations. One combination (P/N/D/Q) gives you an immediate solution. One combination gives you no immediate (can't think of the right word) declaration of a box: N/N/Q/Q.
The other combinations show you either ((the box P/N or the box "
only Q"
) plus a second box) or (P/N and only Q). (I hope that was clear.) As for the rest, you can only draw and wait to get lucky. Obviously, once you get a different coin from one of these boxes, you're done, since you know in advance what the allowable combinations are. The only ways I can think of the maximise your chance of solving the problem quickly is to (i) avoid drawing from a box with quarters, since there is a possibility that the box is the "
only Q"
box, in case you have to wait until you've drawn 50%+1 coins to know for sure which box it is and (ii) always draw from the same box since (due to 50/50 distribution) your chance to get a different coin is greater in the box from which you've drawn most often.
For the one case N/N/Q/Q, you draw from an N box until you've identified those two. In this case, you have identified P/N and N/D, so it would be best to alternate your drawing between the two Q boxes, since one of them will give you no information, as noted above.
--leroy
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You can hear happiness staggering on down the street -- footless, dressed in red.
-Jimi Hendrix, "
The Wind Cries Mary"
]
