India, Sept. 29 -- A recent research paper on how AI approaches mathematical problems provides the basis for the first of this week's puzzles. Mind you, I am not going into what AI did. The puzzle merely picks up the centuries-old problem that AI attempted to solve, with a modification that was necessary to make it look unique. The second puzzle this week is my adaptation of a version I found among Shakuntala Devi's writings.

Puzzle #162.1

A teenager is demonstrating how to draw a square without using a ruler. The only items he uses are an eraser-tipped pencil, a protractor and a divider. With his younger brother as his audience, the teen draws a line guided by the straight edge of the protractor, then marks two points at 90 degrees fro...