Tag Archives: counting

do go no to

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

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

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

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Fermat’s Little Theorem: proof by necklaces

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

[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

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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

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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