Applied math: which egg size is cheapest?
I recently started eating egg whites regularly, and that meant I needed to start shopping for eggs every week. My local grocer sells a variety of egg sizes. Can you figure out which one is cheapest? Here are the prices: Here is how I approached the problem.

An addition/subtraction game
The numbers 1, 2, 3, and 4 are written on a board. Alice writes a "+" or "-" sign in front of one of the numbers, and then Bob and Alice take turns. Once the four signs are written, the arithmetic expression is then evaluated. Bob gets points equal to the absolute ...

Bars and restaurants: often giving you 12 percent less beer since 2008
I was ordering a beer at a restaurant, and I was asked if I wanted the "tall" or a "pint." I suspected the "tall" was a better value, but I always ask to make sure. Occasionally bars will charge a premium on larger quantities, as illustrated in this post on Freakonomics: ...

The Flexible Spending Account: an “investment” with a great “ROI”
Flexible Spending Accounts (FSAs) are an incredible way to pay for health expenses. While FSAs can be complicated and require some effort, I now think their rewards are worth the hassle. I want to explain a bit about how FSAs work, and then I'll get into the math. Most people know ...

Why Skydiving is not safer than driving
I had a hard time accepting that skydiving could ever be considered a low-risk activity. Call me old fashioned, but it just doesn't seem prudent to be jumping out of an airplane with a parachute as your life support. But however I feel personally doesn't really matter. I'm happy to judge ...

A location game on a triangle
A father bequeaths a triangular piece of land to his children, Alice and Bob. The father was known to be quirky, and in his will, he specified a rather unusual way for the land to be divided. On a map of the land, Bob is to mark a location of his choosing. ...

Monday puzzle: fruit label stickers
This is a problem slightly modified from a 2002 Putnam competition question. I thought about this problem while eating a large grapefruit one morning. The puzzle Imagine a perfectly round grapefruit that is labeled with 5 fruit stickers. Prove that the grapefruit can be cut in two equal halves in which one of the ...

What’s the probability of a pure strategy Nash equilibrium?
This is a problem I adapted from the free e-book Algorithmic Game Theory. I had some fun solving it, and so I wanted to share it.

Siegel’s paradox about exchange rates
Exchange rates always seemed simple to me, until I learned a bit more finance. There are some quirky things that can happen, as today's problem will illustrate.

Two math questions from Stanford’s entrance exam in 1892
The Stanford Alumni magazine has a fun article that talks about some of the questions from old, old entrance exams. Some of the questions are ridiculously hard, and I wonder how anyone would have known them back then: Zoology (1892) Give an account of the circulatory and respiratory systems of the clam, the ...

Puzzle: the Riddler vs Batman and Robin
This is a puzzle adapted from Max Schireson's blog. It is based on the trope that villains tend to use elaborate execution schemes. Here is the problem:

When does 1/2 + 2/3 = 3/5?
We all remember how to solve 1/2 + 2/3 in standard arithmetic. You convert each fraction to the least common denominator (6), and find that 3/6 + 4/6 = 7/6. But at times, it can be useful to use a non-standard arithmetic in which 1/2 + 2/3 = 3/5. One example ...

Monday puzzle: the train fly problem
This is a classic math puzzle. Here is the problem:

Game theory of dividing a pizza
Figuring out how to divide a regular pizza is easy. A standard pizza is usually cut into equally-sized slices, so two people can just eat the same number of slices. But what happens when you cut the pizza in odd ways, like the following division? Let's play a game to test your ...

Multiplying with lines math trick: how it works
A friend sent me a video about a multiplication trick. The person draws out a certain number of lines for each number, and then counts out points to determine the answer. It's a bit hard to explain, so watch this video to see the method: