This is an old puzzle from Catriona Agg that I found on BL’s Math Games website.
“All four triangles are equilateral. What fraction of the largest triangle is shaded?”
This problem turned out to be both easy and unexpectedly challenging, at least for me.
See Four Equilateral Triangles for solutions.
This is another Catriona Agg puzzle that I also found somewhat challenging.
“Four squares. What’s the angle?”
Visio showed me the answer fairly soon, but it took a bit to figure out a proof.
See the Rotating Square Problem for a solution.
Since Twitter (now X) is no longer public, I was afraid I would not have access to new Catriona Agg puzzles, but she has put them up on Instagram, which is partially available to the public. I managed to find a half dozen interesting new brain ticklers.
This is a Catriona Agg problem presented by itself, since it turned out to be the most challenging one I ever tried. Usually I can solve her problems in a few minutes or maybe hours, or sometimes days if they are especially challenging. But this problem has taken me weeks and I had to rely on a non-geometric argument. The problem is full of fascinating and unexpected relationships, but I couldn’t find a way to use them to prove the answer.
See the Curious Sunbeam Problem
(Update 5/5/2023, 7/22/2025) Alternative Solutions Continue reading
Here is yet another (belated) collection of beautiful geometric problems from Catriona Agg (née Shearer).
Here is yet another (belated) collection of beautiful geometric problems from Catriona Agg (née Shearer).
This is a most interesting problem proposed by Mirangu and retweeted by Catriona Agg:
“Two equilateral triangles share a vertex. What is the proportion red : green?”
See the Two Equilateral Triangles for solutions.
Here is yet another collection of beautiful, stimulating geometric problems from Catriona Agg (née Shearer).
Here is yet another collection of beautiful geometric problems from Catriona Agg (née Shearer). For some reason I found these a bit more challenging than the previous ones. Some of them required more time to “see” the breakthrough.
See Geometric Puzzle Magnificence (revised)
(Update 11/13/2022) Problem #3 Solution Corrected Continue reading
Here is another collection of beautiful geometric problems from Catriona Agg (née Shearer). They never fail to brighten the day with their loveliness.
