This is another challenging sum from the 2025 Math Calendar.
“Find x where x = 1/y and
”
As before, recall that all the answers are integer days of the month.
See Spring Sum for a solution.
Spring Sum
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Knock the Bottle Problem
This is a problem from Barry Leung’s Math Games.
“Larry and Julius are playing a game, taking turns throwing a ball at a bottle sitting on a ledge. Larry throws first. The winner is the first person to knock the bottle off the ledge. At each turn the probability that a player knocks the bottle off the ledge is ½, independently of what has happened before. What is the probability that Larry wins the game?”
See Knock the Bottle Problem for a solution.
Three Rulers Puzzle
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.
Clockwise Ant Puzzle
This is actually a travel problem masquerading as a clock puzzle from Futility Closet.
“A problem by Argentinian puzzlist Jaime Poniachik, from the February 1992 issue of Games magazine:
An ant crawls onto a clock face at the 6 mark just as the minute hand is passing 12. She begins crawling counterclockwise around the face’s circumference at a uniform speed. When the minute hand passes her, she reverses course and crawls clockwise without changing her speed. Forty-five minutes after her first encounter with the minute hand, it passes her a second time and she departs. How much time did she spend on the clock face?”
See Clockwise Ant Puzzle for solutions.
Ship and Seaplane Puzzle
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.
Integral Challenge
This is a bit of a challenging problem from the 2026 Math Calendar.
“Let f be a continuous real-valued function on the reals. For all t, f(2t) = 3 f(t) and ∫01 f(t) dt = 1.
What is the value of ∫24 f(t) dt ?”
Again, the result must be a number of a day in a month.
See Integral Challenge for a solution.
A Pair of Pretty Perimeter Puzzles
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.
Slanted Volume of Revolution
This is a fairly challenging problem from BL Math Games.
“Find the volume of the solid obtained by rotating the region enclosed by y = x and y = x2 about the line y = x.”
See Slanted Volume of Revolution for solutions.
Trump is a Markov Process
I debated posting this, but it is so rare that a human behavior would be such a perfect example of a mathematical principle that I couldn’t resist. The idea came from a great summary of the state of affairs with Trump by Anne Applebaum in The Atlantic. Continue reading
A Simple Ratio
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.