Weigh #1: A 3, B 6, C 12, D 17, E 16 — the solution

The Weigh set from September 30, 2026: five parcels weighing 3, 6, 12, 16 and 17, par 7. Below, the arrangement and a crack that weighs whatever splits the field best.

The puzzle

Parcels A to E weigh 3, 6, 12, 16 and 17, one each, in a hidden order — one of 120 arrangements. A weighing answers three ways: the left pan is heavier, the right is, or they are level. Par, 7, is the fewest weighings that can always tell them apart.

The walkthrough

At each step, the weighing whose worst answer leaves the fewest arrangements standing — a greedy choice, so it can run a weighing over the optimal plan par was measured on. Here it takes 7, par exactly.

1. A against B — the right pan is heavier. 120 arrangements fit before this weighing; 60 after it.
2. C against D — the right pan is heavier. 60 arrangements fit before this weighing; 30 after it.
3. A against C — the right pan is heavier. 30 arrangements fit before this weighing; 15 after it.
4. A + C against B — the left pan is heavier. 15 arrangements fit before this weighing; 7 after it.
5. A + B against C — the right pan is heavier. 7 arrangements fit before this weighing; 4 after it.
6. A + D against B + C — the left pan is heavier. 4 arrangements fit before this weighing; 2 after it.
7. D against E — the left pan is heavier. One arrangement fits.

The answer

The parcels were A 3, B 6, C 12, D 17, E 16.

About Weigh

Weigh is Noggin’s balance puzzle, on the second shelf: five parcels, five known weights and a balance, solved in as few weighings as par, outside the daily line-up. How to play Weigh, or play today’s.