# Category Archives: counting

## Factorization diagram posters!

I’ve finally gotten around to making a nice factorization diagram poster: You can buy high-quality prints from Imagekind. (If you order soon you should have them before Christmas! =) I’m really quite happy with imagekind, the print quality is fantastic … Continue reading

Posted in arithmetic, counting, geometry, number theory, pattern, pictures, primes | Tagged , , | 7 Comments

## 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

## Animated Sieve of Eratosthenes

Here’s something I made yesterday! (Note, I strongly suggest watching it fullscreen, in HD if you have the bandwidth for it.) Can you figure out what’s going on? The source code for the animation is here; I was inspired by … Continue reading

Posted in arithmetic, counting, pattern, pictures, primes, video | | 12 Comments

## Post without words #3

(This is my 200th post! =)

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

## Some words about Post without words #2

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 | | 4 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

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

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

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 , , | Comments Off on A gentle introduction to the 5th Polymath project