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# Tag 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

Posted in arithmetic, challenges, logic, programming, puzzles, solutions
Tagged arithmetic, binary, denominator, Euclidean, gcd, logarithm, numerator, puzzle, rational, search, wizard

## 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

Posted in arithmetic, challenges, logic, programming, puzzles, solutions
Tagged arithmetic, denominator, Euclidean, gcd, logarithm, numerator, puzzle, rational, wizard
3 Comments

## 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

Posted in arithmetic, challenges, logic, programming, puzzles
Tagged arithmetic, denominator, numerator, puzzle, rational, wizard
15 Comments

## More fun with Dirichlet convolution

I’m back after a bit of a hiatus for the holidays! Last time we saw how the principle of Möbius inversion arises from considering the function from the point of view of Dirichlet convolution. Put simply, the Möbius function is … Continue reading

Posted in number theory
Tagged arithmetic, convolution, Dirichlet, divisors, inversion, moebius, mu
1 Comment

## Right answers for the wrong reasons

Here’s a recent xkcd which as a math educator I found particularly funny. Some questions for my readers: What numbers besides 3 and 9 would “work” here? Do you have any particularly funny or interesting stories of students getting something … Continue reading

## minim

A fun game I discovered recently, minim. In each level you start out with a network of numbered nodes, and the object is to successively combine the nodes according to certain mathematical rules in order to end up with only … Continue reading