Another month, another outpouring of brilliant puzzles from Catriona Shearer.

Apparently she’s going through a semicircles phase, which I’m sure will be remembered with the same fervent enthusiasm as Picasso’s blue period, or the Era of Peak TV, or the year the Beatles got really into acid.

Speaking of which: when will Catriona’s blue period arrive? More urgently, what would tripping acid do for one’s geometric imagination?

Without further ado, six puzzles. Feel free to discuss and solve below.

I spent a week thinking about how to pack two semicircles into a larger one, with very little progress. I only managed to get anywhere when I made a scale drawing. I hoped someone would show me why the solution is obvious; I learned lots from reading the solutions, but it seems it is genuinely tricky.

Most people I showed it to (including my students) managed the correct answer in their first guess but then got into all sorts of a muddle trying to explain why.

I did it with trigonometry, but there are nice ways without – such as this.

I wrote a solution for The Broken Purple Moon problem. Enjoy the pretty diagrams!

https://latex.artofproblemsolving.com/miscpdf/ujbsbvey.pdf?t=1579199137864