# Puzzles

## Disappearing Area?

We’ve been looking at dissection puzzles, where we cut an object into pieces, and rearrange them. Here we’ll examine a mystery posed by two different puzzles, each of which seems to change the area by rearranging the pieces. The answer combines the marvelous Fibonacci numbers and [spoiler alert!] how easily we misjudge areas.

## Cutting and Rearranging a Rectangle

Last week we looked at a puzzle about cutting a square cake into equal pieces. Here we will be trying to cut a rectangle into two pieces and rearranging them to make a different rectangle. Three of the questions we’ll look at came within two weeks in 2001, but we’ll take them in a logical …

## Cutting a Square Cake Equally

For the next couple weeks, we’ll look at a few “dissection problems”, which involve cutting a shape in various ways. Here, we look at what turns out to be a simple problem, though it seems at first that it would be complicated: dividing a cake into pieces with the same amount of cake and the …

## 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 …

## “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 …

## 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 …

## Four Fours and Friends

This has been a good time for doing puzzles to stay busy (as a family, or a class, or as distanced friends, for instance). The next few posts will present various mathematical puzzles and games you might enjoy. Although often when a problem I quote was originally left unsolved, I have filled in the gap …

## The Locker Problem

A classic problem we’ve seen hundreds of times involves students opening and closing lockers. I have often told people that, believe it or not, they could find the answer by searching the Ask Dr. Math site for the word “locker”. But I prefer to give them a reference to one of the answers in which …