Comments on: The Cookie Monster Problem
https://blog.tanyakhovanova.com/2011/04/the-cookie-monster-problem/
Mathematics, applications of mathematics to life in general, and my life as a mathematician.Sat, 27 Sep 2014 01:56:34 +0000
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By: Pratik Poddar
https://blog.tanyakhovanova.com/2011/04/the-cookie-monster-problem/#comment-2002
Tue, 03 May 2011 19:26:28 +0000https://blog.tanyakhovanova.com/?p=325#comment-2002Another interesting variant.

Let there be (2^k-1) jars numbered 1 to (2^k-1). The jar numbered i contains ai+b cookies (a and b are non-negative integers). Again, by the same logic used above, cookie Monster can empty it in k moves. ðŸ™‚

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By: JBL
https://blog.tanyakhovanova.com/2011/04/the-cookie-monster-problem/#comment-2001
Tue, 26 Apr 2011 14:54:45 +0000https://blog.tanyakhovanova.com/?p=325#comment-2001Wait, here’s “the” “right way” to think about what’s going on: given any set of numbers, subtract 1 from all the odds (if any); then subtract 2 from all those that are twice an odd (if any); then subtract 4 from those that are four times an odd (if any); and so on. This is essentially the same as your strategy for {1, 2, …, n} but it gives in general an upper bound of “the number of distinct powers of 2 that appear in the binary representations of all the elements of the set”, or (weaker) the ceiling of log-base-2 of one more than the largest number in the set. (Sometimes of course we can do better than this, e.g., if every number in the set 2 more than a multiple of 4 is actually 6 more than a multiple of 8, we can squish two steps into one.)
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By: JBL
https://blog.tanyakhovanova.com/2011/04/the-cookie-monster-problem/#comment-2000
Mon, 25 Apr 2011 12:28:14 +0000https://blog.tanyakhovanova.com/?p=325#comment-2000Very cute — so fast-enough exponential growth is some sort of a barrier. I guess two natural questions are, “Suppose the sequence of size weights is given by a polynomial (or is “close” to a polynomial in some sense to be determined) — is the bound still logarithmic?” and “What about Fibonacci boxes?”
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