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 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.
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.
