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Topic: Glass Balls (Read 4881 times) |
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Garzahd
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The other puzzle went over well, so I'll try another one that I like. (Forgive me if I've got the wrong forum; this could also be classified in CS, since it's originally from topcoder.com's programming contest. But I think it's more a problem-solving/math problem than a programming one.)
You have B identical glass balls, and an F story building. You want to find out how resilient the balls are. You know there exists some floor N<=F, such that a ball dropped out a window of floor N will not break, but a ball dropped from floor N+1 will break. (N may be 0, in which case all dropped balls will break.)
You want to find N in as few drops as possible. What's the worst-case number of drops you must use to find N, given B and F?
Clarifications: Dropped unbroken balls may be recovered and dropped again. Once N is found, it doesn't matter how many unbroken balls you have remaining, only the number of drops it took you to get there.
A couple hidden sample cases (depending on how much of a challenge you want):
With 1 ball and 42 floors, 42 drops are required.
With 2 balls and 100 floors, 14 drops are required.
With 3 balls and 92 floors, 8 drops are required.
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| « Last Edit: Oct 23rd, 2003, 7:40pm by Icarus » |
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Garzahd
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Re: New Puzzle: Glass Balls
« Reply #2 on: Oct 11th, 2002, 2:47pm » |
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Man, I suck. I would have sworn I had read all those. Sorry about that.
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