This is a puzzle from Boris Kordemsky’s 1972 Moscow Puzzles.
“Two freight trains, each 1/6 mile long and traveling 60 miles per hour, meet and pass each other. How many seconds is it between when the locomotives pass each other and the cabooses pass each other?”
See Trains Meeting for solutions.
From Presh Talwalkar here is a variation of the three jugs problem.
“You have buckets that hold 3 L, 7 L, and 20 L of water. How can you measure the following amounts?
For most of mathematical history the above information would be sufficient information to state the problem. But in today’s society, there is a demand to state all assumptions as if that will make the problem better. So the test explained there are certain actions you can take.
You can fill any bucket completely with water. You can pour all the water from a bucket into a larger bucket. You can pour water from a bucket to fill a smaller bucket. You can empty the water completely from any bucket.”
See the Three Buckets Question for solutions.
A recent video by Angela Collier about compound interest reminded me of an effort I did years ago to derive the formulas for interest calculations, especially for installment payments on a loan like a mortgage. In the process I showed where Euler’s constant e can show up. I thought I would resurrect the material, even though I imagine modern texts now provide the information (I couldn’t easily locate it back then).
This is another problem from BL’s Math Games.
“What fraction of the rectangle is colored? Assume that M and N are midpoints of the sides of the rectangle.”
That they are midpoints was not stated explicitly in the problem as given in front of the subscription wall, but from the comments it became evident this was the case.
Initially I actually assumed the line was positioned arbitrarily. What would be the solution in that case?
Answer to BL problem.
See ZigZag in Rectangle for a solution.
This problem is from BL’s Math Games.
“What’s the area of the red triangle?”
BL decided to see what kind of solution ChatGPT would come up with. After several tries and prompts it seemed to oblige. I don’t know what BL’s prompts were, and in the statement of the problem outside the subscription wall he never explicitly says what the problem is, namely, to find the area of the red triangle.
There also seems to be some ambiguity about the constraints on the problem, that is, how much of the appearance of the diagram should the solver assume?
See ChatGPT Problem for a solution.
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?”
See the Spot in a Rectangle Problem for a solution.
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)”
See Yet Another Track Puzzle for a solution.
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.
See Two Radical Problems for solutions.
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.
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.
