Weigh Order

Six crates, all different weights, and a two-pan scale that answers exactly one question: of these two, which is heavier? You choose the pairs. You get twelve answers. Fifteen pairs exist, so three of them have to come from thinking rather than weighing — once the scale says A beats B and B beats C, the A-against-C question is already answered, and the grid marks it implied without you spending anything. The round ends the instant your answers leave exactly one possible order standing.

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 around the grid with the arrow keys. Every square is one pair: the crate lettered down the side against the crate lettered along the top. The squares on the diagonal are a crate against itself, so they are dead.
3. Press Enter or Space to put that pair on the scale. The square fills in with the letter of the heavier crate and the word weighed underneath it.
4. Watch the implied squares appear. Every square the answer forces fills in at the same moment, marked implied. Those were free. The count of orders still standing — 720 at the start — drops with each weighing, and that drop is the only thing you are buying.
5. Press F to jump straight to the next pair nobody knows yet. That never costs a weighing.
6. Ask for something already known and the scale refuses it rather than charging you. It tells you which chain of earlier weighings already answered the question — that refusal is the whole lesson, so it is worth reading rather than clicking past.
7. Finish before twelve weighings are gone. When the last pair fills in, exactly one order fits and you have won. Run out first and the round ends with the answer shown.

How many weighings does it take to put six things in order?

Ten, in the worst case, and no strategy can do better. The reason is a counting argument rather than a clever trick: a two-pan scale answers with one of two outcomes, so W weighings can produce at most 2 to the power of W different answer sequences, and each sequence can name at most one order. Six crates can be arranged 6 factorial = 720 ways, and 2 to the power of 9 is only 512 — not enough sequences to name 720 orders — while 2 to the power of 10 is 1024, which is. So the floor is 10, and that floor is known to be reachable. The practical strategy that comes closest without being fiendish is binary insertion: keep a run you have already sorted, and place each new crate into it by halving — weigh the newcomer against the middle of the run, then against the middle of whichever half survives. That costs at most 11 here, which is why this game gives you 12.

Why do some squares fill in on their own?

Because heavier-than is transitive. If A is heavier than B and B is heavier than C, then A is heavier than C, and no scale is needed to establish it. The grid works out every consequence of every answer the moment it arrives, so a square you never asked about can settle itself — those are the ones marked implied. There are always more than people expect, and getting more of them is the entire skill: 12 weighings have to cover 15 pairs, so at least three facts must arrive free.

Which pairs can never be implied?

The neighbouring ones. If two crates sit next to each other in the true order, nothing sits between them, so no chain of the form "A heavier than X, X heavier than B" can ever reach across the gap. Those five pairs must each be weighed directly, whatever you do. That is a useful thing to know while playing: a weighing between two crates you suspect are neighbours is never wasted, and a weighing between two you already believe are far apart very often is.

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

None, and there never will be. No currency, nothing to buy, no hints to unlock for a fee, no prizes.

Does it work offline?

Yes. Once the page has loaded once, the whole game is on your device — the board, the scale, the transitive closure that fills the implied squares, and the counting solver that decides when exactly one order is left. No server is involved in play at any point.

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

Both. Arrows move around the grid, Enter or Space weighs the pair under the cursor, F jumps to the next pair nobody knows. Every square announces itself as a sentence — "A against D: D is heavier than A, implied" — and the live region reports how many orders still fit, how many weighings are left and what the last press did. The state of a square is carried by the letter printed in it and the word underneath, so nothing depends on telling two colours apart.

What is the score made of?

A base for pinning the order, plus 60 for each weighing you did not need, plus a bonus for finishing inside 10 — the theoretical floor, which takes a real strategy rather than luck. Losing scores nothing. The result card also shows how many of the fifteen pairs you got for free.

Six crates, so 720 possible orders and 15 pairs. The budget is fixed at 12 weighings: the information-theoretic floor of 10 plus a margin of 2, chosen so that binary insertion — a strategy a person can actually carry out — always fits, since its worst case here is 11. The true order is drawn before anything else, so every answer the scale gives is consistent by construction and no board can be contradictory. Weights are never shown as numbers; only comparisons exist, which is the point. There is no undo: a weighing tells you something true, so there is nothing to take back.

Balance Scale is the other weighing puzzle here — it hunts one odd crate out of many, where this one orders them all. Gap Logic turns on relational clues you are given rather than ones you buy, and Rank Sort asks you to arrange rather than to deduce.

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