Gap Logic

Six cells, the digits 1 to 6, each used once. The clues never say where a digit is — only how the digits sit relative to one another: 3 is somewhere left of 5, 1 and 2 are next to each other, 4 and 6 have exactly two cells between them. Swap digits around until every clue reads a tick. Exactly one arrangement can do that, and it is proven before the board is dealt — so you never have to guess, and no clue on the list is spare.

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 along the row with the left and right arrows. The small number under each digit is the cell it is sitting in, which is what a "two cells between them" clue is counted in.
3. Step through the clues with the up and down arrows. The focused clue puts a dashed edge on the two cells it names, so you can see exactly what it is talking about.
4. Press Enter on a cell to pick its digit up — a ◆ appears in the corner — then Enter on another cell to exchange the two. Only the exchange spends a swap.
5. Press Esc to put a picked-up digit back. Changing your mind is always free.
6. Watch the ticks. Every clue shows ✓ or ✗ against the row as it stands right now. When the last ✗ turns to ✓ you are finished, because no other arrangement satisfies them all.

How do you work out an order from clues like "3 is left of 5"?

Start with the clue that forbids the most, not the one that names the most digits. A clue about a gap is the strongest thing on the list: on a six-cell row, "exactly four cells between them" leaves only cells 1 and 6, and "exactly three cells between them" leaves only two pairs of cells. Pin those first, then use left of clues to decide which way round each pair goes — a left-of clue never places anything on its own, it only ever halves what is left. Adjacency clues are next strongest: a pair that must touch behaves like one two-wide block that can slide, so counting where that block can fit usually kills most of the remaining arrangements in one go. Work down from strongest to weakest and the answer falls out without a single guess.

Is there always exactly one answer?

Yes, and it is proven rather than assumed. The answer is drawn first and every clue is read off it, so no clue can contradict the answer. The list is then trimmed by a solver that walks all 720 arrangements: a clue is thrown away only if what remains still fits exactly one arrangement. What you get is both unique and irredundant — put any discarded clue back and nothing changes, but take any clue you can see away and a second arrangement becomes possible.

Why can I only swap digits, instead of typing them in?

Because the row starts as a complete arrangement, "each digit used exactly once" is true by construction — you can never strand yourself with two 4s and no 6, which is the most common way a puzzle like this goes wrong. It also makes the budget meaningful: the game knows the shortest possible route from the deal to the answer, so the swaps you are given are that number plus three. Work out the answer first and the leftmost-first route — put the correct digit into cell 1, then cell 2, and so on — always finishes inside it.

What happens when the swaps run out?

The round ends and the answer is shown. That is the only way to lose, and it is there to stop shuffling standing in for thinking: with six digits there are 720 arrangements, so rearranging until something works is not a strategy. Nothing else costs you anything — picking a digit up, putting it back, reading the clues and moving around are all free and unlimited.

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 — the board, the clue generator and the solver that proves the answer is unique — is on your device. No server is involved in play at any point.

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

Both. Arrows move along the row and through the clue list, Enter picks up and exchanges, Esc puts a digit back. Every cell announces its number, its digit and whether it is picked up; every clue is announced as a sentence with satisfied or not satisfied after it. A picked-up cell carries a ◆, clued cells carry a dashed edge and each clue carries ✓ or ✗, so nothing on the board depends on telling two colours apart.

Six cells and six digits, so 720 possible arrangements — small enough that uniqueness is checked exhaustively at generation time rather than estimated. A trimmed list runs to four to six clues in practice, of three kinds: left of, immediately left of, and exactly n cells between. The swap budget is the shortest possible route from the dealt row plus three spare, and the dealt row is always at least three swaps from the answer — so the tightest boards give you six swaps and the loosest eight.

Grid Clues is the other deduction puzzle here — it turns on overlap where this one turns on order. Light Grid is the third, and turns on parity.

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