Tag Archives: counting

Penn Alexander: subset counting and Gray codes

Posted on November 2, 2010 by

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

Posted on July 27, 2010 by

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

Posted on April 17, 2009 by

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 →

Posted in challenges, counting | Tagged , , | 8 Comments

Distributing cookies: solutions

Posted on April 14, 2009 by

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 →

Posted in counting, proof, solutions | Tagged , , , , , | 4 Comments

Chessboard counting: solutions and further challenges

Posted on March 30, 2009 by

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 →

Posted in challenges, counting, solutions | Tagged , , , , | 2 Comments

Chessboard counting

Posted on March 13, 2009 by

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

Posted on January 31, 2009 by

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

Posted on April 18, 2008 by

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