This is a cute little problem from Presh Talwalkar.
“A parent was stumped by his 10 year old’s homework, and posted it to Reddit AskMath. A box contains 3 rulers, as shown. If the blue ruler is 1 cm shorter than the green ruler, what is the length of the yellow ruler?”
See Three Rulers Puzzle for solutions.
This is a puzzle from Boris Kordemsky’s 1972 Moscow Puzzles.
“A diesel ship leaves on a long voyage. When it is 180 miles from shore, a seaplane, whose speed is ten times that of the ship, is sent to deliver mail. How far from shore does the seaplane catch up with the ship?”
See Ship and Seaplane Puzzle for solutions.
Here are two puzzles from Alex Bellos’s Monday puzzles.
“Ring it. Each region has a perimeter given by its enclosed number. What is the length just along the edge of the entire figure?
Round the block. Assuming all corners are right angles, what is the perimeter?
Today’s puzzles all come from … the Hyde Park Math Zine! This delightful publication is written in pen on a single folded sheet of paper, has a print run of 30 copies, and is distributed in the neighbourhood of Hyde Park in Austin, Texas.
Fanzine culture is well established in sports and music. Math educator Kevin Gately thought the format would work for puzzles too. “It dawned on me that there might be people in my community who find the novelty of a hyper-local math zine to be amusing and/or curious,” he said. And it seems there are.
Each issue of HPMZ presents three problems, with easily understandable answers, and let’s not forget the cover artwork! Gately’s puzzles are mostly taken from other sources, and tweaked. Here are [two] that took my fancy.”
See A Pair of Pretty Perimeter Puzzles for solutions.
This is a straight-forward problem by Ritvik Nayak from the Puzzle Sphere.
“Evaluate the ratio. It’s actually simpler than you might think.”
Apparently it is a sample problem from the Southeast Asian Math Olympiad (SEAMO).
See A Simple Ratio for solutions.
This is a problem from the 2001 American Invitational Mathematics Exam (AIME).
“Each of the 2000 students at a high school studies either Spanish or French, and some study both. The number who study Spanish is between 80 percent and 85 percent of the school population, and the number who study French is between 30 percent and 40 percent. Let m be the smallest number of students who could study both languages, and let M be the largest number of students who could study both languages. Find M – m.”
See Language Students Problem for a solution.
This is a problem from Presh Talwalkar.
“Given that x satisfies the equation:
x4 + x3 + x2 + x + 1 = 0
What is the value of
(x33 + 2/x22)(x22 + 3/x33)”
See Root of the Problem for solutions.
This is a simple puzzle from Futility Closet.
“Mr. Smith goes to Atlantic City to gamble for a weekend. To guard against bad luck, he sets a policy at the start: In every game he plays, he’ll bet exactly half the money he has at the time, and he’ll make all his bets at even odds, so he’ll have an equal chance of winning and of losing this amount. In the end he wins the same number of games that he loses. Does he break even?”
See Smart Money for solutions.
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.
