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.

“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 …

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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 …

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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 …

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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 …

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