Balance Scale

A case of numbered weights, and exactly one of them is heavier than the rest. A pan balance will tell you which side went down — never by how much — and you have a small budget of weighings to work out which weight it is and name it. The board keeps score of how many weights are still consistent with everything you have seen, so a weighing that teaches you nothing is visible the moment you make it.

It runs entirely on your device: 0 network requests, works offline. No ads, no account, nothing to buy, and no betting, money or prizes of any kind.

1. Focus the board — click it, or press Tab until it is focused.
2. Move with the arrow keys. Left and right wrap around the strip, which runs through the weights and ends with the two controls.
3. Load a pan with Enter. Each press moves the weight under the cursor one step: off the scale, then the left pan, then the right pan, then off again.
4. Weigh with F, or move to the Weigh control and press Enter. Both pans must hold the same number of weights.
5. Read the count. After each weighing the board shows how many weights are still possible. That number is the whole game — if it does not drop, the weighing was wasted.
6. Name it. Move to Name the heavy weight, press Enter, then press Enter on the weight you are committing to. You get one answer, so make it a deduction rather than a guess.

How do you find the heavier weight with a balance scale in the fewest weighings?

Split the weights that are still possible into three near-equal groups, put two of the groups on the pans, and weigh. There are exactly three things the balance can say, and each one points at one group: left down means the heavy weight is on the left, right down means it is on the right, and level means it is in the group you did not weigh. Whatever happens you are left with about a third of what you started with, so repeating that is the fastest possible search. Because each weighing has three answers, W weighings can tell apart at most 3 to the power of W weights — so nine weights need two weighings, twelve need three, and no cleverness gets below that floor. Halving instead of thirding, which is what most people do first, throws away a third of every weighing.

Why must the pans hold the same number of weights?

Because otherwise the fuller pan goes down no matter which weight is heavy, and the result tells you about the count rather than about the weights. Equal counts are what make the balance a question about the odd weight at all. The game refuses an uneven weighing instead of spending one on it.

What does "still possible" mean?

It is the number of weights that would produce every result you have seen so far, if that weight were the heavy one. It starts at the full case and drops as you weigh. Watching it stall is the fastest way to learn what an uninformative weighing looks like — for instance, weighing two weights you have already ruled out cannot change it at all.

Is every deal actually solvable in the weighings I am given?

Yes, and it is checked rather than hoped for. The budget is the information-theoretic minimum for that many weights — the smallest W with 3 to the power of W at least as large as the case — plus one spare weighing. Before a deal is handed to you, the solver plays the three-way split against it and confirms it finds the answer inside that budget. A deal that failed would never reach the board.

Why does the scale not tell me how much heavier it is?

Because a balance compares, it does not measure. It has two pans and a beam; the only thing it can report is which side went down. That limitation is the reason the puzzle is interesting, and it is why the excess in grams is only revealed at the end.

Is there any money, betting or in-app purchase in this?

None, and there never will be. There is no currency, nothing to buy, no wager of any kind and no gambling mechanic anywhere in the game — it is a logic puzzle about a set of weights.

Does it work offline?

Yes. Once the page has loaded once, the whole game is on your device: the weights, the rules and the solver. Nothing is sent anywhere while you play, and there is no server involved at any point.

Can I play it with a keyboard or a screen reader?

Both. Arrows move, Enter loads a pan or commits, and F weighs. Every weight announces which pan it is on and whether it is still possible, and the live region reads out the result of each weighing along with the count that is left. Each pan is marked with an arrow glyph and a word, so nothing depends on telling one colour from another.

Nine to sixteen weights, exactly one of them heavier, and a budget of the information-theoretic minimum plus one spare weighing. A comparison you have already made is refused rather than charged for, in either direction, because its answer is already known. Naming the wrong weight ends the round, and so does spending the last weighing with more than one weight still possible.

Light Grid is the other deduction game here — it asks you to plan a sequence of moves whose effects cancel, rather than to narrow a field of suspects.

Bookmark this page (Ctrl+D, or ⌘D on Mac) or install the app — it works offline the next time you need it.