Tag Archives: counting

PIE day

[This is part six in an ongoing series; previous posts can be found here: Differences of powers of consecutive integers, Differences of powers of consecutive integers, part II, Combinatorial proofs, Making our equation count, How to explain the principle of … Continue reading

Posted in combinatorics, counting | Tagged , , , , | 2 Comments

Penn Alexander: subset counting and Gray codes

I’m volunteering again this year with the middle school math club at Penn Alexander. I’m going to try to be better this year about posting what we do each week, for posterity’s sake and in case it inspires anyone else! … Continue reading

Posted in counting, pattern | Tagged , , , , | 1 Comment

More cookies

I recently received the following interesting problem from Shadowcat, which is a generalization of the cookie problem I’ve written about previously. We again want to count the ways to distribute identical cookies to non-identical students, with the twist that we … Continue reading

Posted in arithmetic, challenges, counting | Tagged , , | 9 Comments

Idempotent endofunctions

Via Topological Musings comes another neat little counting problem. A function is idempotent if applying it twice gives the same result as applying it once: that is, for any input x. Endofunction is just a fancy way of talking about … Continue reading

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Distributing cookies: solutions

And now for some solutions to the cookie distribution problem. I’m actually going to describe four different methods of solution, and thereby (re)discover some nice combinatorial identities along the way. This is what I love about combinatorics—you discover all this … Continue reading

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Chessboard counting: solutions and further challenges

And now for some solutions to the chessboard counting challenges. The first challenge was to count the number of squares of any size on an 8×8 chessboard. The key here (as with many counting problems) is to break the problem … Continue reading

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Chessboard counting

I am currently doing a unit on combinatorics (the mathematical study of counting) with my precalculus students, and I was inspired to post a few counting-themed challenge problems for your enjoyment. (Also, it’s my spring break!) As you probably know, … Continue reading

Posted in challenges, counting | Tagged , , , , | 10 Comments

Carnival of Math #48, and Monday Math Madness #25

The 48th Carnival of Mathematics is posted at Concrete Nonsense. My favorite posts include Foxmath’s post about a strange iterated sequence involving pi and this amazing picture of a fractal cabbage. Also near and dear to my heart is Mark … Continue reading

Posted in challenges, counting, famous numbers, fractals, links | Tagged , , , , | 1 Comment

Challenge #12: sums of powers of two

A few interesting problems for you to think about: Given a positive integer n, in how many ways can n be written as a sum of powers of two, when each power is allowed to occur at most once? For … Continue reading

Posted in challenges, counting, pattern | Tagged , , , | 18 Comments