Category Archives: challenges

Challenge: area of a parallelogram

Posted on June 24, 2021 by Brent

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 →

Posted in challenges, geometry | Tagged , | 18 Comments

The Natural Number Game

Posted on May 25, 2021 by Brent

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 , , , , , | 6 Comments

A probabilty puzzle

Posted on July 15, 2019 by Brent

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 →

Posted in challenges, probability | Tagged , | 9 Comments

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

Posted on November 9, 2018 by Brent

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 , , , , , , , , , , | Comments Off on The wizard’s rational puzzle (solutions, part 2)

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

Posted on October 24, 2018 by Brent

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 , , , , , , , , | 3 Comments

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

Posted on August 7, 2018 by Brent

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 , , , , , | 15 Comments

The curious powers of 1 + sqrt 2

Posted on June 6, 2017 by Brent

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 →

Posted in challenges, number theory, puzzles | Tagged , , , | 15 Comments

Fibonacci’s Problem of the Birds

Posted on April 1, 2017 by Brent

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 →

Posted in algebra, arithmetic, challenges, people | Tagged , , | 6 Comments

The route puzzle

Posted on June 17, 2016 by Brent

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 , , , , , , | 7 Comments

Post without words #5

Posted on February 5, 2016 by Brent
Posted in challenges, pattern, pictures, posts without words | 4 Comments