Determining whether a number is prime (or “The Benefits of Square-Rooting a Number, Part I”)

Something that comes up now and again in various contexts during lessons is how to tell whether a number is prime. My usual advice has been to use divisibility rules*, and if none work, then it's likely that the tested number is prime. Likely is not the same thing as certain, however, and, as the … Continue reading Determining whether a number is prime (or “The Benefits of Square-Rooting a Number, Part I”)

Solving tracing problems using graph theory

A couple of weeks ago, I was looking at a standardized test and came across the following “tracing” problem: Which of the drawings below can you completely trace without lifting your pencil or retracing a previously traced part?  When I was a teenager, I had seen similar questions to this one, but was always frustrated … Continue reading Solving tracing problems using graph theory