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## Finding the Counterfeit Coin

I wrote about a brain teaser I encountered as a kid and challenged you to figure out if it has a solution, and if so, what that solution is. That brain teaser works like this: You have 12 identical coins. One of them is counterfeit. The counterfeit coin may be heavier...

## The Toughest Brain Teaser

People seem to like the brain teasers I’ve posted. So here’s another. I first ran across this when I was about 12 years old. I still remember it as one of the toughest brain teasers I ever faced. It is a very simple problem to explain, but the answer may...

## Pythagorean Triplets and Diophantine Equations

Last week I posed a challenge that came from my high school computer teacher: Can you find an efficient method (or “algorithm”) to generate Pythagorean triplets? As a reminder, a Pythagorean triplet is a set of three integers that satisfy the Pythagorean...

## Brain Teaser: Finding Pythagorean Triplets

In an earlier post I wrote about a brain teaser from middle school. Here’s one that is a bit more advanced. My high school computer teacher issued us a challenge: “I want you to write an algorithm to identify Pythagorean triplets.” At the time, I...

## Brain Teaser: Proof That 2 = 1

This is a classic brain teaser I learned in middle school (or “junior high school” where I grew up). Let’s prove that: Here’s the proof: Let’s start by establishing some variables: Okay, so if that’s true, then we know: In algebra,...