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.
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.
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.
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?”
See the Hangover Clock Reading for a solution.
This problem from A+Click follows a classic pattern.
“There are 190 coconuts in a basket. Sailors one after another take out half of them and one each time until one is left. How many sailors are there?
Answer Choices: 5 6 7 8”
See Sailors and Coconuts for solutions.
This is a math Olympiad problem from Puzzle Sphere where Muhammad Zain Sarwar claims it is at Harvard entrance exam level.
“Given the functional relationship f(x + y) = f(x) + f(y) + xy with the known value f(4) = 10, determine the value of f(2023).”
Just try some examples and detect the pattern that defines the function.
See the Functional Equation Puzzle for a solution.
Here are two algebra problems from the 2025 Math Calendar.
“#1. Find the value of the ratio
#2. Find the value of the sum
z90 + z87 + … + z3 + 1
where z2 + z + 1 = 0.”
Remember the answers are days on the calendar.
See Two Algebra Puzzles for solutions.
This is a fairly straight-forward problem from A+ Click.
“The water from an open swimming pool evaporates at a rate of 5 gallons per hour in the shade and 15 gallons per hour in the sun. If the pool loses 8,400 gallons in June and there were no clouds, what is the average duration of night during that month?”
Answer Choices: 6 hours 8 hours 10 hours 12 hours
See Evaporating Pool Problem for solutions.
This is a classic puzzle from Presh Talwalkar.
“This puzzle has been asked as an interview question at tech companies like Google.
There are 100 lights numbered 1 to 100, all starting in the off position. There are also 100 people numbered 1 to 100. First, person 1 toggles every light switch (toggle means to change from off to on, or change from on to off). Then person 2 toggles every 2nd light switch, and so on, where person i toggles every ith light switch. The last person is person 100 who toggles every 100th switch.
After all 100 people have passed, which light bulbs will be turned on?”
I vaguely remembered the answer, which I confirmed after a few examples. But I didn’t remember an exact proof, so I thought I would give it a try.
See 100 Light Bulbs Puzzle for solutions.
This is another take on the passing train type puzzle from the Moscow Puzzles.
“A train moving 45 miles per hour meets and is passed by a train moving 36 miles per hour. A passenger in the first train sees the second train take 6 seconds to pass him. How long is the second train?”
See Another Passing Train Puzzle for solutions.
