Split Bill

A table of nine dishes has arrived as a single bill, and everybody has agreed to pay the same amount. The share is printed above the board and it is not a rounded-off suggestion: it is exactly one third of the bill, to the last paisa. Your job is to decide who pays for which dish so that all three running totals land on that number at the same time.

Every dish already belongs to somebody when the board opens, so there is never a half-filled bill and never a dish nobody is covering. The only move is to hand one dish across the table, and each hand-over is one move out of a small budget. That budget is not a guess either — the board works out the fewest hand-overs that could possibly settle this bill and then adds three, so a route always exists and there is never much room to wander.

The bill is built backwards. Three finished shares are made first, each one broken into three prices, and only then are the nine prices shuffled together into the list you see. That is why a fair split is guaranteed before you have looked at anything: the board is showing you a settled bill with the labels taken off. Prices are also pinned close enough together that four dishes can never fit inside one share, so everybody finishes holding exactly three — a handrail that cuts the search in your head roughly in half.

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. Read the share. It is printed above the bill and it never changes. Every person has to finish on that exact figure; there is no rounding and no "close enough".
3. Press the up and down arrows to move between the nine lines. The line you are on is outlined, and the board says which dish it is, what it costs, and who is paying for it now.
4. Press the left and right arrows to choose a person. The three names sit in the same order on every line, so the second column is always the same person.
5. Press Enter or Space to hand that line to the chosen person. The line changes hands, both totals move at once — the giver drops by the price, the receiver rises by it — and one move comes off your budget. The W, S, A and D keys mirror the arrows.
6. Or click straight onto the board. Every line has one small button per person; clicking one hands that dish over at once. One click is one move, exactly like one press.
7. Handing a dish to the person already paying for it is free. Nothing changes and nothing is spent, so a mistaken press never costs you anything.
8. Watch the three standings. Each person shows their total and how far they are from the share — "exact", "over by" or "short by". Two people over and one short means the short one has to receive, and the amount they are short is the price you are looking for.
9. Press F, or either Shift key, or the Check the bill button, when you think it is right. If all three totals equal the share, the bill is settled and the round is won. If not, it costs one check, and you only have a few.
10. If your last move lands the bill equal, it settles itself. Running out of moves on a bill you have just balanced would be a strange way to lose, so the board does not do that to you.
11. The round ends when the bill is settled, when the moves run out, or when the checks run out. Either way the board then shows a split that would have worked, line by line.

How do you split a restaurant bill so everyone pays the same?

Work from the share, not from the items. Add the whole bill up, divide by the number of people, and treat that figure as a target each person has to hit — then the question stops being "who ate what" and becomes "which group of items adds to the target". The practical method is to fix one person at a time: find any combination that reaches the share exactly, set those items aside, and repeat on what is left with one fewer person. The last person needs no work at all, because if everybody before them landed on the share then whatever remains must add to it too. That is the whole trick, and it is why this game shows every running total live: the moment one person is exact you can stop thinking about them and shrink the problem. The other habit worth building is to think in differences rather than totals — if somebody is 40 over and somebody else is 40 short, the single item worth 40 that sits with the wrong one of them settles both of them at once.

Why does moving one dish change two totals?

Because a dish never leaves the table, it only changes hands. Whoever had it drops by its price and whoever receives it rises by the same price, so the pair of totals moves apart by twice the price while the sum of all three totals stays exactly on the bill. That is worth internalising, because it tells you which move to look for: if one person is 90 over and another is 90 short, you do not want a dish worth 90 — you want a dish worth 45, since handing it over closes a gap of 90. And it explains why the total of the three standings is always zero — every rupee somebody is over is a rupee somebody else is short.

Is a fair split always possible?

Always, by construction rather than by luck. The board builds three complete shares before it builds the bill: it picks the share, breaks it into three prices, does that three times, and only then shuffles the nine prices into one list. The grouping it started from is a valid answer to the puzzle it hands you, so at least one exists before you have pressed anything. Most bills have several. How many is worked out exactly — the board walks every way of assigning nine dishes to three people and counts the ones that settle — and a bill with very many ways is thrown away and re-drawn, because a puzzle you can stumble into is not a puzzle. The count is also what sets your number of checks: the fewer ways there are to settle a bill, the more attempts you get.

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

None, and there never will be. The prices are printed numbers in an arithmetic puzzle — nothing is paid, nothing is owed, nothing is collected and there is nothing to buy. There are no prizes, no currency of any kind, and no way to risk anything on the outcome. Your results stay in your own browser and go nowhere else.

Why does everybody end up with exactly three dishes?

Because the prices are deliberately kept in a narrow band: the cheapest dish on any bill is more than a quarter of the share, so four dishes always cost more than one person owes. Nobody can hold four, and nine dishes shared between three people who can hold at most three each leaves exactly three apiece. That is a genuine handrail rather than a hint — you can rule out every grouping of two or four before you start, which removes most of the search. It is also what keeps the count of possible splits small enough for the board to work out exactly instead of estimating.

Does it work offline, and can I play it with a keyboard or a screen reader?

Yes to all three. Once the page has loaded once, everything runs on your device — the generator that builds the shares, the solver that counts the ways to settle the bill and sets your move budget, and the arithmetic that updates three totals after every hand-over. No server takes any part in play. The whole game works with the arrow keys, Enter and F alone, and every line announces its dish, its price and who is paying; every person announces their total and whether they are exact, over or short. Nothing is carried by colour: each person has their own initial, each state has its own symbol and its own word, and the amounts are written out in full.

What happens if I run out of moves or checks?

The round stops and the board shows you a split that would have settled the bill, line by line, next to the one you finished with. Losing on moves means you spent the budget wandering; losing on checks means you settled too early too often. Both are recoverable habits, and seeing the answer beside your attempt is usually enough to spot which dish you should have moved first — it is almost always the one whose price matches the gap between the person who is over and the person who is short.

Nine dishes, three people and one share, always. Every price is a multiple of five rupees and every amount is held as whole paise, so a bill balanced to the last paisa is compared exactly and never rejected by rounding. Prices sit in a narrow band by design, which is what forces three dishes each and keeps the exhaustive count of splits cheap; it also means the bills never look wildly uneven, and a puzzle where one item dwarfs the rest is one you will not see here. There is no timer, no hint button and no undo — handing a dish back costs a move like any other, so a wrong move is paid for rather than erased. The move budget is the exact minimum plus three, so there is room for one wrong idea and not two. The people are fixed names in a fixed order and do not have preferences; this is an arithmetic puzzle about equal shares, not a negotiation, and it does not model tips, taxes or anybody paying a different amount on purpose.

Cut Share is the other puzzle here about landing several running totals on one figure, from the other direction — you move the boundaries rather than the items. Weight Split is the two-way version of the same arithmetic and is where the habit of thinking in differences starts. Pair Sums and Sum Links are the quick drills for spotting which two numbers make a target, which is the sub-problem you solve over and over here. Ledger Check is the other game built on whole paise and exact equality, and Magic Square is the one where every group has to hit the same total at once, so no group can be fixed on its own.

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