I’m looking at various common puzzles, and ways to think about them logically. Today, we’ll examine basic magic squares: not the standardized methods you can look up, but how a kid can work them out when seeing them for the first time. Often they are not even told they have a name, so there is …
Here is another puzzle we have received and answered many times. (I count 7 that have been archived.) It has several variations, which make it even more interesting. The story varies, too; sometimes the monkeys are the stars, other times they just get the leftovers. Someone could to an interesting folklore study on this one.
We often compare math problems to puzzles; and some puzzles are math problems. I want to devote a couple posts to interesting puzzles that can be attacked in various ways. Here, we are given the weights of every possible pair of hay bales, and have to work out the individual weights. This classic can be …
(A new question of the week) Today we’ll look at a problem that puts a little twist on the basic idea of translating a graph. The focus is on finding alternate approaches to the problem, which is an important skill in problem solving.
(An archive question of the week) I’m going to do something unusual, and post a discussion that was never archived. I ran across it while searching for the original of an archived discussion to check something, and this one stood out as worth posting around the start of the school year. It’s a question from …
(A new question of the week) Last week we looked at a recent question about basic trigonometric equations. That discussion continued into the subject of identities, which we’ll look at here. We’ll be sitting in on an extended chat about many important aspects of this kind of work. It’s still very long, even after extensive …
(An archive question of the week) While I’m showing some recent explanations of basic trigonometry techniques, this is a good time to look at an even more basic explanation of the essentials of the subject for a beginner.
(A new question of the week) This week and next I will look at a recent discussion on trigonometry that dug deep into two different issues: solving equations, and proving identities. These are good summaries of how to approach these common kinds of problems. This week: solving basic trig equations.
Since we just looked at a complicated rational inequality, let’s look at some simpler rational equations, first a linear equation with fractions, and then truly rational equations, in which the variable(s) appear in the denominator. This discussion dealt with a common confusion I’ve seen in students.
When a challenging type of problem is written with unexpectedly large numbers, it can look impossible. Today’s discussion illustrates how to get past the hurdles.