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.”
See the Three Circles Problem 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.
An article by Lee Moran in Huffpost is rather remarkable. Apparently someone failed grade-school math. I wonder how he got through medical school, especially the pharmacology course.
“NBC News’ Kristen Welker on Wednesday asked Mehmet Oz — the former talk show host and heart surgeon who now runs the Centers for Medicare and Medicaid Services — about President Donald Trump’s repeated claim, mockingly dubbed “MAGA Math,” that he’ll get pharmaceutical companies to lower drug prices by more than 100%. Continue reading
These code-breaking puzzles are from MathsJam Shout for October 2025. The second one is reminiscent of the mesmerizing 1970s game Mastermind, which consumed many hours of my time.
See Two Codebreaking Puzzles for solutions.
This is another problem from Dan Griller.
“In the triangle ABC, CN and MB are straight lines, ÐCAB = 90° and CM = MA = AN = NB = 5. Find the exact area of the shaded region.”
See the Triangle Bow-tie Problem for a solution.
This is an earlier puzzle from Presh Talwalkar.
“A square pyramid has base PQRS and vertex O. Each edge has length equal to 20. Calculate the shortest distance along the outer surface of the pyramid from P to T, the midpoint of OR.”
See Shortest Pyramid Path for solutions.
