Category Archives: arithmetic

The wizard’s rational puzzle (solutions, part 2)

At long last, here is the solution I had in mind for the Wizard’s rational puzzle. Recall that the goal is to figure out the numerator and denominator of a secret rational number, if all we are allowed to do … Continue reading

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The wizard’s rational puzzle (solutions, part 1)

About two and a half months ago I posted a challenge involving a sadistic math wizard, metal cubes containing rational numbers, and a room full of strange machines. I’ve been remiss in following up with some solutions. (Go read the … Continue reading

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Quickly recognizing primes less than 1000: memorizing exceptional composites

In my previous post I wrote about a procedure for testing the primality of any number less than : Test for divisibility by all primes up to , and also . (In practice I test for 2 and 5 first, … Continue reading

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Quickly recognizing primes less than 1000: divisibility tests

I took a little hiatus from writing here since I attended the International Conference on Functional Programming, and since then have been catching up on teaching stuff and writing a bit on my other blog. I gave a talk at … Continue reading

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Quickly recognizing primes less than 100

Recently, Mark Dominus wrote about trying to memorize all the prime numbers under . This is a cool idea, but it made me start thinking about alternative: instead of memorizing primes, could we memorize a procedure for determining whether a … Continue reading

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Post without words #22

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The wizard’s rational puzzle (mind your p’s and q’s!)

You have been abducted by a sadistic math wizard (don’t you hate it when that happens?). He ushers you into a plain but cozy-looking room, with a hardwood floor, a few exotic-looking rugs, and wood paneling on the walls. He … Continue reading

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