Linkage

Real-world application of square packing: Packing ten quart bottles in a milk crate slightly larger than a \(3\times 3\) packing. Significant increases in perceived cheating, and decreased willingness of honest students to turn in cheaters, lead Stanford and Princeton to give up on honor code based unproctored exams (\(\mathbb{M}\), via). Ars Technica blames the cheating on AI, but although it seems likely to me that the ease of cheating with AI is a factor, I’m skeptical that it’s the root cause. Belgian public transport company De Lijn promote themselves via a QR code that looks like a metro map. Triple cover of a \(4\times 5\) rectangle by the twelve pentominoes poses challenges for visualization. The original posting by Alexandre Muñiz uses diagonal stripes with three colors per unit square; the comments include an animated version adding black outlines to each tile, and a couple of ball-and-stick diagrams. On the classification of quadrilaterals and the visualization of the…