The Doppit Almanac · No. 50

Weighit, a daily balance puzzle

Hang every weight so each bar balances

What it is

Weighit is a Doppit original, No. 50 in the almanac. A mobile hangs from an anchor: a bar, and wires dropping from that bar to a pan or to another bar. Every bar prints the arm of each wire hanging on it. Numbered weights wait in a tray, and a board can open with a few of them already hung or with the tray still full.

A weight pulls with its number times the arm it hangs at, and a bar balances when the pull on its left equals the pull on its right. A bar hanging under another pulls on that one with everything below it, so a weight at the bottom pulls on every bar above it. Anyone who has sat on a see-saw knows that sitting further out pulls harder.

How it plays

The difficulties

Easy hangs six pans and six weights. Read one bar, ask what the rest of it can pull, and usually one weight is all that still fits the pan you are looking at. Nothing on easy asks you to suppose anything. Medium is eight pans and eight weights, and once a board at most you have to suppose. Put a weight on a pan, follow what it forces, and wait for a rule to break: a bar left with nothing in the tray that can balance it, say. Then that weight is out. Hard is twelve pans and twelve weights and wants that move two to four times. Expert is sixteen and sixteen, and asks for it at least five times. A fresh mobile hangs every day, for nothing.

Play today's board