# Month: November 2018

## Permutations and Combinations: Undercounts and Overcounts

(A new question of the week) We have been looking at some combinatorics questions, both easy and challenging. Some questions have come to us in recent weeks that can illustrate how to think your way through relatively difficult problems, including catching errors and interpreting a textbook’s solutions. We’ll see yet again that there are usually …

## Six Distinguishable People in Four Distinguishable Rooms

(An archive question of the week) Last time we looked at some elementary problems in combinatorics, where we counted the number of ways to choose or arrange elements of a set. Let’s look at a somewhat more complicated problem, which will demonstrate issues that come up in interpreting such a problem and in choosing a …

## Permutations and Combinations: An Introduction

We have seen a number of questions recently about combinatorics: the study of methods for counting possibilities. These topics are studied at all levels of mathematical education, from elementary (where they might just be called counting) to high school (where they are often learned along with probability) to college (where they are part of “discrete …

## A Different Kind of Chessboard Problem

(A new question of the week) Looking through recent answers we’ve given, I realized that one shares several features with my last post, as both involved proving facts using modular arithmetic and the pigeonhole principle. I need to do posts specifically about both of those concepts soon. For now, you can use the references I …

## A Very Different Kind of Sequence

(An archive problem of the week) While gathering sequence/pattern questions for my last post, I ran across a very different problem. Here we are told what the pattern is (a good example of one that you would probably never discover on your own), and asked some questions about later terms. It can be understood either …

## Pattern and Sequence Puzzles Revisited

Back in May, I wrote about pattern and sequence puzzles, and didn’t have the space to cover all that I would have liked. It’s time to revisit the topic, looking at a couple different types of sequences, and then the “input/output” or “function” puzzles that add an extra twist to the idea.

## Distances to an Arc: Exact and Approximate Formulas

(A new question of the week) It can be an interesting challenge to be presented with a formula and asked how it was derived. This becomes a bigger challenge when the formula is only approximate, so we have to figure out how to arrive at this particular approximation. But it is impressive when several different …

## Three Times Larger: Idiom or Error?

Having just written about issues of wording with regard to percentages, we should look at another wording issue that touches on percentages and several other matters of wording. What does “three times larger” mean? How about “300% more”? We’ll focus on one discussion that involved several of us, and referred back to other answers we’ve …

## Talking About Percentages

A recent discussion with a student I was tutoring face to face, about an ambiguously worded problem, led me to gather a few answers we’ve given related to the words we use associated with percentages.

## Greatest Common Divisor: Extending the Definition

Having just talked about definition issues in geometry, I thought a recent, short question related to a definition would be of interest. We know what the Greatest Common Divisor (GCD, also called the Greatest Common Factor, GCF, or the Highest Common Factor, HCF) of two numbers is; or do we?