Tag Archives: counting

do go no to

Posted on January 7, 2020 by Brent

dodo do go on do no harm do to others go do likewise go-go music go no further goto considered harmful no can do it’s a no go a big no-no say no to drugs what to do here or … Continue reading →

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A new counting system

Posted on December 30, 2019 by Brent

0 = t__ough 1 = t_rough 2 = th_ough 3 = through So, for example, trough through tough though though. English is so strange.

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

PIE: proof by counting

Posted on August 13, 2019 by Brent

Recall the setup: we have a universal set and a collection of subsets , , , and so on, up to . PIE claims that we can compute the number of elements of that are in none of the (that … Continue reading →

Posted in combinatorics, pattern, proof | Tagged , , , , | 1 Comment

Fermat’s Little Theorem: proof by necklaces

Posted on December 12, 2017 by Brent

It’s time for our second proof of Fermat’s Little Theorem, this time using a proof by necklaces. As you know, proof by necklaces is a very standard technique for… wait, what do you mean, you’ve never heard of proof by … Continue reading →

Posted in combinatorics, number theory, primes, proof | Tagged , , , , , , | 4 Comments

PIE day

Posted on October 15, 2013 by Brent

[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

Posted on November 2, 2010 by Brent

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 Brent

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 Brent

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 Brent

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 Brent

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