Eratosthenes Measures the Earth

Last time we looked at a couple questions about proving the earth is round, which led into questions about how Eratosthenes measured the earth (though that in itself did not prove the earth is not flat). Let’s look at two questions about that project itself. Eratosthenes for third graders The first is from 1995, and …

Eratosthenes Measures the Earth Read More »

Impossible? Try anyway!

(An archive question of the week) Here’s a little problem with some big lessons for problem solving. Not enough equations? This question is from Kenanga in 2017, not long before the Ask Dr. Math service stopped taking questions: Insufficient Information In Question Given A + B + C = 1 B + C + D …

Impossible? Try anyway! Read More »

Bayes and Virus Testing

News about testing for viruses has reminded me of a couple problems that I linked to some time ago, but never dealt with directly. The question is, given data such as the result of a (fallible) blood or swab test, how sure can we be of the results? The answer is sometimes surprising. False positives …

Bayes and Virus Testing Read More »

“Order of Operations” Puzzles

We have often received questions about things called “Order of Operations problems”, or some similar name. Generally, what that means is simply that they are puzzles to give lots of practice evaluating expressions using the order of operations. I have collected a few quite different puzzles in this broad category. A free-form expression We’ll start …

“Order of Operations” Puzzles Read More »

The 24 Game and Kin

We are looking at various mathematical puzzles and games, with a focus on discussing rules and strategies, and then letting you play. Last time we discussed Four Fours, in which we are given a fixed set of “inputs” to a calculation (usually 4, 4, 4, 4), and want to find expressions that yield as many …

The 24 Game and Kin Read More »