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Category Archives: challenges
Challenge: area of a parallelogram
And now for something completely different!1 Suppose we have a parallelogram with one corner at the origin, and two adjacent corners at coordinates and . What is the area of the parallelogram? There are probably many different ways to derive … Continue reading
The Natural Number Game
Hello everyone! It has been quite a while since I have written anything here—my last post was in March 2020, and since then I have been overwhelmed dealing with online and hybrid teaching, plus a newborn (who is now almost … Continue reading
Posted in challenges, computation, proof
Tagged computer, game, Lean, natural, number, proof
6 Comments
A probabilty puzzle
Suppose that we have surveyed a certain population of people, and have determined the following probabilities: The probability that a person likes anchovies is . The probability that a person likes to read books is . The probability that a … Continue reading
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
Comments Off on The wizard’s rational puzzle (solutions, part 2)
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 cozylooking room, with a hardwood floor, a few exoticlooking 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
The curious powers of 1 + sqrt 2
Recently on mathstodon.xyz, Colin Wright posted the following puzzle: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? Of course, it’s simple enough to use a computer to find the answer; any … Continue reading
Fibonacci’s Problem of the Birds
I have been enjoying reading Keith Devlin’s new book, Finding Fibonacci. I’ll write more about the book later. For now, I just wanted to share a nice problem I learned about which Leonardo Pisano, aka Fibonacci, included in his book … Continue reading
The route puzzle
While poking around some old files I came across this puzzle: (Click for a larger version.) I didn’t make it, and I have no idea where I got it from (do you know?). But in any case, wherever it comes … Continue reading
Posted in arithmetic, challenges, number theory, proof, puzzles
Tagged cube, perfect, prime, puzzle, route, square, triangular
7 Comments