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Decision Making: The Missing Link in AI

Recent advances in AI have taken the world by storm. OpenAI’s release of ChatGPT introduced the world to Large Language Models, which do a great job of mimicking interaction with people. Ask it a question, and it seems to “get” you, and generally gives a pretty...

Bonjour!

In the US as well as in the UK, I hear complaints that the French are rude—particularly Parisians in the service industries, such as restaurant waiters. On the other side, Parisians sometimes make the same complaint of the tourists who come to town—and there are a lot...

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...