Author Archives: Jim Stevenson

Spot in a Rectangle Problem

This puzzle is from the Irishman Owen O’Shea.

“The following puzzle illustrates a beautiful mathematical relationship involving a rectangle of any size and a random point within that rectangle that most people, including mathematicians, are unaware of.

The figure shows a rectangular room. There is a matchbox located 6 feet from one corner of the room and 27 feet from the opposite corner. The matchbox is also located 21 feet from a third corner.

How far is the matchbox from the fourth corner?”

Answer.

See the Spot in a Rectangle Problem for a solution.

Yet Another Track Puzzle

This is another problem from Dan Griller.

“When Anthony and Benjamin run round a circular track in the same direction at constant but different speeds, they meet every 3 minutes. When Benjamin changes direction (but maintains his speed) they meet every 40 seconds.

If Anthony is faster than Benjamin, calculate

(speed of Anthony) / (speed of Benjamin)”

Answer.

See Yet Another Track Puzzle for a solution.

Two Radical Problems

Here are two problems involving those pesky radicals from the 2025 Math Calendar.

“#1. Find the value of the expression

#2. Find the value of x in the expression

Incredibly the answers are days on the calendar.

Answer 1 _____ Answer 2

See Two Radical Problems for solutions.

Exponential Growth Story

Raza Abbas at 3QuarksDaily linked to a post on X by Magnus Hambleton which Abbas titled, “Which Door Would You Choose?”.

This is a fascinating, fun story about exponential growth and computers, in particular computer arithmetic, which I have annotated a bit for those less familiar with some terminology:

“I chose the green door ninety-three days ago.

At the time, it seemed obviously correct. Not even a close call. The red door offered two billion dollars immediately—a sum so large it would solve every material problem I’d ever face, fund any project I could imagine, and still leave enough to give away amounts that would meaningfully change thousands of lives. But two billion is a number. It has a fixed relationship to the economy, to the things money can buy, to the world.

The green door offered one dollar that doubles every day.

I remember standing there, doing the mental math. Day 30: about a billion dollars. Day 40: over a trillion. Day 50: a quadrillion. The red door would be surpassed before the first month ended, and after that, the gap would grow incomprehensibly fast. Choosing the red door would be like choosing a ham sandwich over a genie’s lamp because you were hungry right now.

So I walked through the green door.”

See an Exponential Growth Story.

Mixed Emotions

This is a brainteaser by S. Ageyev from the November-December 1991 issue of Quantum given in Futility Closet.

“The numbers 1, 2, …, 100 are arranged in a 10 x 10 square table in their natural order (1 in the top left comer, 100 in the bottom right comer). The signs of 50 of these numbers are changed in such a way that exactly half of the numbers in each line and each column get the minus sign. Prove that the sum of all the numbers in the table after this change is zero.”

See Mixed Emotions for solutions.

Three Circles Problem

This is a problem from the 1995 AIME problems.

“Circles of radius 3 and 6 are externally tangent to each other and are internally tangent to a circle of radius 9. The circle of radius 9 has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord.”

Answer.

See the Three Circles Problem for solutions.

Hangover Clock Reading

This is another clock puzzle from the 1978 Eureka magazine.

“The hands on my alarm clock are indistinguishable, and there are no numbers around the outside. Accidentally woken up by it one morning, I observed with a snarl that the hands were both pointing at minute divisions, and that they were 9 minutes apart.

Had it not been for my hangover, what could I have deduced?”

Answer.

See the Hangover Clock Reading for a solution.