The other day, I came across this problem on Twitter: How many distinct ways are there to color the vertices of a cube, such that exactly four are one color and the other four are a second color? I played around a bit first. My first task was to list all the possible combinations, and…
Category: Puzzles and Memes
Questioning, Not Answering
Another Rant on “Mathematical” Puzzles A few months ago, I complained about those internet memes which claim to be mathematics. My complaint about them is about the presentation, not the underlying problems: “Only 1% of people get this right!” The questions are framed to encourage people to feel stupid about math. Please don’t feel stupid about math….
Witches, Candy, Monkeys, and Math
Mathematics isn’t about finding answers. It’s about asking questions. As a mathematician, here’s a question I usually find boring: What’s the answer? Consider this manifestation of a sort of meme that wanders the internet: The most likely intended answer is 73, just to get that out of the way. I’ll call this “Witch”. This is…
The Math Meme That Would Not Die
Some version of this question keeps getting asked on the internet. What is \(8\div2(2+2)\)? Some background The strength of mathematical notation is at the intersection of clarity and simplicity. We could be completely clear, which would leave us writing details we don’t need and make it hard to read. We could oversimplify, and lose clarity….
The Game of Set
The game of Set consists of 81 cards. Each card has one, two, or three identical symbols of one of three shapes (oval, diamond, or squiggle), in one of three colors (red, green, or purple) and one of three textures (solid, hollow, striped). A “set” consists of three cards where each of the four attributes…
The Free Throws Problem Part 2
Here’s an extension to the problem in my previous post. Time has run out, and a player is at the free throw line. If he makes the first shot, he gets a second try. If he makes both shots, his team wins; if he misses the first, his team loses. Otherwise, it’s a tie game,…
But is it math?
It is a persistently popular thing to do on social media to post challenges like this one. I used to be of a mind to be outraged at the abuse of the equal sign: Clearly these are not addition problems! This is not how math symbolism works! This is not math! However, I’ve since shifted…
Inscribed Right Triangle
(Edit 6/18/23: The image has been lost, but I’ll leave the text in case I ever have the chance to reconstruct it.) Here’s a fun puzzle (via Brilliant.org): What is the area of the square \(ABCD\)? There may be a simpler approach; my solution wound up being more complicated than I expected. Since \(\Delta AEF\)…
Dan Meyer’s Really Really Really Difficult Puzzle
Dan Meyer offered this puzzle. The essence of it is, given an arbitrary number for volume, can we build an algorithm that will always generate the integer side lengths that give us the least surface area? He put it in more “real world” terms than that, but that’s the gist. If we did it in two…
Filling in Blanks: The General Case
Discussion about the puzzle behind the previous post led to this question: Is it possible to construct a similar question, where there are three of five values and a mean given, and where the median is half one of the missing values, with has exactly two solutions? That is, given the values {a, b, c,…