so i previously came up with a solution but it was too boring and literally just 2 lines of actual instructions, admittedly in a made up language but still...
so instead i propose a mechanical solution to the problem.
imagine if you will:
a crank and to two sets of gearing with pointers on the end, one dividing by 3, the other by 5, and a third connected to an odometer at a 1:1 ratio.
usage:
spin the crank a number of times corresponding to your number.
when the pointers are pointing up, its fizz or buzz respectively, or fizzbuzz if its both. otherwise just read the number off of the odometer.

👍