Sum Links

Sixteen digits sit in a four-by-four grid, and the board asks for one thing: a line of exactly four or five touching cells whose numbers add up to the stated total. Every cell in the line must share an edge with the one before it — no diagonals, no jumps, and no cell used twice. Each board is built around a line that already works, and every other line reaching the same total is counted before you see it, so the game can tell you how rare your answer was.

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. Read the two numbers above the board — the total to reach, and how many cells the line must hold. Both are fixed for that board.
2. Focus the board — click it, or press Tab until it is focused.
3. Move the cursor with the arrow keys, or WASD. The cell under the cursor is outlined, not just tinted.
4. Take a cell with Enter. It joins the line and shows its position: #1, #2, and so on.
5. Follow the small arrows. Every cell you may take next prints what you would still need after taking it — →7 means seven left to find. A neighbour that would carry you past the total is greyed and reads over, and cannot be taken at all.
6. Take a cell back by pressing Enter on it again while it is the last one in the line, or press Esc to clear the line and start again. Both cost nothing.
7. Check the line with F, or the Check line button. A line of the stated length that totals the target wins the round; anything else costs one of your tries.
8. Watch the tries. A board with a single answer gives you six of them, a crowded board three. Run out and the round ends — and one line that would have worked is marked on the board.

How do you find a run of numbers on a grid that adds up to a target?

Work from what is left, not from what you have already added. Subtract each cell you take from the target and carry the remainder instead of the running total: the question at every step becomes "which of my neighbours is small enough to fit, and does what is left still divide sensibly among the cells I have to spare?" That single change kills most of the board immediately. With three cells left and 6 to find you cannot use anything above 4, because the other two cells hold at least 1 each; with one cell left, only an exact match will do. Sum Links prints that remainder on every legal neighbour so the arithmetic is visible rather than remembered, which is also why a dead end here shows up one cell before you commit to it instead of after.

Is every board actually solvable?

Yes, and by construction rather than by luck. The line comes first: the generator walks four or five touching cells at random, gives them values, and the target is their sum — so an answer of exactly the stated length exists before a single other cell has been filled in. Filling the rest of the grid can add more answers but cannot remove that one. The finished board is then handed to a separate counter that walks every self-avoiding line of that length and counts the ones that hit the target; it never looks at the line the generator built, so finding at least one is a genuine check rather than an assumption, and the test suite runs it over thirty seeds.

Why is one board worth more points than another?

Because the game knows exactly how many answers each board has. After the grid is filled, every line of the right length is walked exhaustively — the whole search space is at most 832 steps, so this is instant — and the distinct sets of cells that reach the target are counted. That number is shown to you as Routes, and it drives everything: a board with one route pays twelve times what a board with a dozen routes pays, and it also hands you six tries instead of three. Difficulty here is measured from the solver's own work, never guessed by a designer.

Do diagonals count, and can a line cross itself?

No to both. Two cells are linked only when they share an edge, so touching at a corner is not touching, and a cell that is already in the line cannot be taken again. Those two rules are what make the puzzle a line rather than a subset: plenty of sets of four cells add up correctly and simply cannot be traced. A 2x2 block is the clearest example of the opposite case — no cell in it has three neighbours inside the block, yet all four can be traced in one line by going round.

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

None, and there never will be. The numbers are digits on tiles: no currency, nothing to buy, no wager of any kind, and no gambling mechanic anywhere in the game. The score exists so a good board is worth more than an easy one, and it buys nothing.

Does it work offline?

Yes. Once the page has loaded once, the whole game is on your device — the board generator, the route counter, the rules and this copy. Nothing is fetched while you play, and no result leaves the device.

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

Both, and with the same rules rather than a reduced set. Arrows or WASD move the cursor, Enter takes a cell and takes it back, F checks the line, Esc clears it. Every cell announces its value and what it can do right now — "can be added, leaving 7 to find", "too big for what is left", "chosen, position 2" — and the board announces the total, how much is left, how many cells are still to place and how many tries remain. Nothing anywhere depends on telling one tint from another.

Four by four, digits 1 to 9, and a line of exactly four or five cells — stated on the board, never guessed. A line shorter than two cells cannot be checked at all, and a cell that would push the running total past the target is refused rather than punished, because the board already showed you it would. Boards are drawn up to six times and the scarcest is kept, so most have one to four answers; the counter stops at 64, which no generated board comes close to. There are no hints and no undo history beyond stepping back through the line you are tracing.

Target 24 is the other arithmetic search here — four numbers, four operations, one total — and it verifies every hand before dealing it, exactly as this verifies every board. Knight Hop is the other game about tracing one path that may never revisit a square. Mini Sudoku and Prime Sweep are the other number games, and both are about eliminating what cannot be true rather than guessing what might be.

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