Monthly Mindbenders: Solutions

Independent solutions to Peter Winkler's Monthly Mindbenders for the National Museum of Mathematics. Each chapter states the problem with attribution, solves it from scratch, and closes with the program that confirms the answer. The problems reward one clean idea rather than machinery, which is what makes them worth writing up.

A working draft, one chapter a month. Nine so far, from January to September 2026: a ladybug on a clock face, bacteria that cannot escape a box, two subsets with the same sum, ten points under disjoint disks, fifty strings tied at random, a hundred random chords, six dice showing four distinct faces, pegs that cannot reach a corner, and a telephone number that divides a string of ones. The pleasure of the column is how often the right weighting or the right symmetry replaces a calculation entirely. The bacteria are trapped by giving the point $(x,y)$ weight $2^{-(x+y)}$; the ladybug’s answer is $1/11$ because on a cycle every vertex except the start is equally likely to be last.