Department of Mathematics
Undergraduate Problem Solving Competition

Problem 2 (10/21 - 11/4) - Glass orbs

a) You're doing tolerance testing on new high-strength crystal balls. You want to find out how much height they can be safely dropped from. You've been given two of these orbs, and you intend to drop them off various floors of a 5-story office building. The floors are numbered from 1 to 5, with floor 1 being ground level, and you may drop either of the orbs from any floor you wish. Once one of your orbs breaks, you can't reuse it. You're guaranteed that both of the orbs will break at a certain floor and both won't break below that floor. What is the minimum number of drops you need to perform to find out what the most height the orbs will survive is?

b) What about if you still have two orbs, but the company's offices have moved into an n-story building?

c) How about n floors and k balls? What if you think about the problem in reverse - that is, how many floors can you cover with k balls and n drops? Any further generalizations are, as always, welcome.

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