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.
This is another problem from A+Click.
“As each of five eggs is weighed, the average weight increases by one gram each time. If the first egg weighs 50 grams, what is the weight of the last egg?
Answer Choices: 55 grams 56 grams 57 grams 58 grams”
See Weighing Eggs for solutions.
I thought this puzzle, which was included among a set of seven challenges assembled by Presh Talwalkar, would be fairly straight-forward.
“A cube of 50 cm is filled halfway with water. A rectangular prism with a square base of 25 cm and a height around 50 cm is placed flat onto the base of the cube, as shown. By how much does the water level rise?
Thanks to Fahad Alomaim for the suggestion! This is translated from a Mawhiba curriculum question for 8th grade.”
But I got the wrong answer and found Talwalkar’s solution a bit hard to fathom at first. Looks like I flunked 8th grade.
See Brick in Water Puzzle for solutions.
This is a somewhat unusual problem from Presh Talwalkar. It involves proving a student’s homework problem is impossible.
“I came across a homework problem described as “scary” on Reddit AskMath. You need to fill in the number sentences using the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 exactly once.
You should try a few possibilities to see why this is a challenging question. And do not waste too much time because the exercise is literally impossible! The challenge is, can you prove no solution exists?”
See Impossible Homework for a solution.
This is a fun puzzle from John Bassey at Puzzle Sphere.
“The diagram shows a heptagon with three circles on each side. Some circles already have the numbers 8 to 14 filled in, while the remaining circles need to be filled with the numbers 1 to 7. Each circle must contain one number, and the sum of the numbers in every set of three circles along a line must be the same. Arrange the numbers!!!”
See Fill in the Blanks for a solution.
