The Piano Key Width Conundrum: A Linear Programming Puzzle

Have you ever noticed that the widths of the white keys on a piano aren't all the same? This isn't an accident, but rather an interesting linear programming problem. The article explores how to minimize the variation in the widths of the back ends of the white keys, given that the black keys have uniform width and the front ends of the white keys are all the same width. Several common piano key designs are analyzed, culminating in an optimized solution that divides the octave into 878472 units, achieving remarkably small discrepancies in both white and black key widths.