Category Archives: counting

Post without words #3

Posted on October 29, 2011 by

(This is my 200th post! =)

Posted in counting, pattern, pictures, posts without words, recursion | 11 Comments

Some words about Post without words #2

Posted on September 11, 2011 by

My previous post displayed this picture: As Yuriy Kashnikov guessed, I made this picture using diagrams, a Haskell library I am developing for creating images like this. (You can see the source code for this picture here.) If you haven’t … Continue reading →

Posted in counting, pascal's triangle, pattern, pictures | Tagged , , , , | 4 Comments

Post without words #2

Posted on September 6, 2011 by
Posted in counting, pascal's triangle, pattern, pictures, posts without words | 10 Comments

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

Optimal change-carrying

Posted on June 24, 2010 by

Recently Michael left the following challenge in a comment: I’ve been trying to optimize my change-carrying habits. What is the smallest amount of quarters, dimes, nickels and pennies one can carry while still being able to give perfect change (two … Continue reading →

Posted in arithmetic, challenges, counting | Tagged , | 11 Comments

A gentle introduction to the 5th Polymath project

Posted on April 21, 2010 by

I highly recommend reading Jason Dyer’s description of the Erdős discrepancy problem, the subject of the most recent Polymath project (the Polymath projects are an experiment in massively collaborative mathematics, where anyone at all can contribute something towards a solution). … Continue reading →

Posted in arithmetic, counting, links, number theory, open problems | Tagged , ,

Challenge #12 solution, part II

Posted on September 19, 2009 by

Yes, that’s right, that Challenge #12, posted one year, five months, and a day ago. You see, I have this nasty habit of starting things and not finishing them… well, better late than never! Question two of the aforementioned challenge … Continue reading →

Posted in challenges, counting, induction, pattern, sequences, solutions | Tagged , | 15 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