This is a puzzle by Nnamdi Samuel from Think Art.
“The pink circle is tangent to two sides of the square and its diagonal, and the purple semicircle is also tangent to the side of the square and its diagonal. Which area is bigger, the circle or the semicircle?”
See Circular Areas Puzzle for solutions.
This is a Harvard University geometry puzzle from BL’s Math Games.
“These are two circles of radii 3 and 5. The black line of length 10 connects the centres of the two circles. The blue line is a common tangent to both circles. The question is: what’s the length of the blue line?”
See Tangent to Circles Problem for a solution.
This is a problem from Federico Kereki in Puzzle Sphere.
“In this puzzle, we start with a quarter circle (from a circle with center P) and a semicircle. The PQ tangent from P to the semicircle is 9 units long. What is the area of the orange rectangle?”
See Two Arcs Puzzle for solutions.
Yet another puzzle from Presh Talwalkar.
“I thank Taka for the suggestion! He created the puzzle and posted it to Twitter.
In rectangle ABCD, side AB = 8. There are two circles: one tangent to AB and BC (and has point E), and another tangent to AD and CD (and has point F). The two circles are also tangent to each other. The line EF is parallel to AB, passes through the tangent point, and EF = 6. What is the length of BC?”
See the Boxed Circles Problem for a solution.
This is a problem from BL’s Math Games that was on a 2012 Oxford Admission Test.
“If two chords QP and RP on a circle of radius 1 meet in an angle θ at P, then the largest possible area of the shaded region RPQ is
(a) θ(1 + cos θ/2)__(b) θ + sin θ__(c) (π/2)( 1 – cos θ/2)__(d) θ”
See the Oxford Max Area Question for a solution.
This is a fun problem (#1455) from A+ Click.
“Gerry and Jane are at the foot of a conical-shaped mountain with a direct way to the peak of 8 km and the foot circle’s diameter of 8 km. They walk from point A to the diametrically opposite point B by the shortest route. Find the distance c from the foot of the mountain to the highest point of their route C.
Answer Choices:__2.34 km__2.66 km__3.34 km__3.66 km”
See Conical Mountain Climb for solutions.
This is another stimulating puzzle from the July 2026 MathsJams Shout, this time by Andy Parkinson.
“What is the area of the hexagon? What is the perimeter?”
See Hex Flex Puzzle for a solution.
This is a simple problem from the 2026 Math Calendar.
“Find the area of the rectangle.”
Again, the result must be a number of a day in a month.
See Area of Rectangle for solutions.
This is an interesting Talwalkar problem from 2021.
“Thanks to Lucas from Brazil for the suggestion! This problem is adapted from a Kangaroo Maths competition in 2020 for grades 9-10 (around 15 years old).
A circle has diameter AB. A line starts at A and zig-zags exactly 4 times between the diameter and the circumference until it ends at B, as shown.
If each of the angles the line makes with the diameter has the same measure α, what is α equal to?”
See the Zigzag Line Problem for a solution.
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.
