Weekend Diversion: The Logic That Stumped Brooklyn Nine Nine
Ethan Siegel

You missed a simpler solution. Let’s say U is unknown and unweighed, L is possibly-Light, H is possibly-Heavy, and M is definitely-Medium weight.

Second weigh is LLHH/LHMM or UU/UM. Third weigh is LH/MM or U/M. You only have U when all weighs so far have been balanced.

This gives a nice consistent simplification.— Alsee