# Month: May 2020

## 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.

## Proving the Earth is Round … or Not

Can you use mathematics to prove that the earth is round? That’s a question we get from time to time, sometimes from people who want to prove the earth is flat, sometimes from people who want to convince their friends otherwise, and sometimes just from students. Let’s think about it.

## Impossible? Try anyway!

(An archive question of the week) Here’s a little problem with some big lessons for problem solving.

## 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.

## Invariants for a State Machine

(A new question of the week) Although we focus in this blog on questions at early college level and below, we do get questions at higher levels. This one deals with finding an invariant for a finite state machine, with possible movements of a robot as the example.

## Logic Puzzles: Who Owns the Fish?

Having looked at methods for solving four logic puzzles, I’ll close the series with a classic, this one involving five houses, five colors, five countries, five drinks, five cigarettes, and five pets – that’s six attributes to juggle! (Last time, we had only 3 or 5.) Once again, the challenge is to solve it without …

## Logic Puzzles: Five Murders, Five Friends

Here are two more logic puzzles similar to those we looked at last time. Each is partly solved, enough to teach how to approach such problems (this time, using tables), but leaving enough of a challenge for you to finish up. What’s new here is that we will be using tables to keep track of …

## Logic Puzzles: Five Jars, Five Teams

We have received a number of questions about various kinds of logic puzzles. This week I want to collect several for which we gave hints or partial solutions that demonstrate in detail how to think, without taking away all the fun. These all involve a set of people or objects that have a set of …