Grid Zen: sudoku solving techniques that never need guessing

One rule, checked three ways

Every tile in Grid Zen belongs to three groups at once: its row, its column and its 3×3 box. The rule is that each of those nine-tile groups needs every digit from 1 to 9 exactly once, no repeats. Tap a tile to select it and the game lights up its row, column and box for you, along with every other tile already holding the same digit — which is the game doing the first, most tedious part of sudoku by hand for you.

That highlighting is worth using deliberately, not just glancing at. Before placing a digit, look at what's already lit: if a 7 is lit in the row, the column and the box, that tile cannot be a 7, and you've just eliminated one of nine possibilities without any guessing at all. Do that for a few digits and a tile's real options usually shrink to one or two very fast.

The two techniques that solve most of the puzzle

On the early levels — Grid Zen leaves more than forty digits already filled in at that end of the ladder — almost everything solves with two ideas. The first is a single candidate: look at one empty tile, cross off every digit that already appears in its row, column or box, and if only one digit survives, that's the answer. The second is a single position: look at one digit instead of one tile, and check where in a row, column or box it could still legally go. If every tile but one is already ruled out, that tile has to be it.

These two techniques are really the same elimination viewed from two directions — tile-first or digit-first — and switching between them is what keeps a puzzle moving when one angle stalls. A tile that looks ambiguous from its own row can be pinned down instantly once you check the same tile from its box, or from the digit's perspective instead of the tile's.

When clues thin out: pointing pairs and naked pairs

Further up the ladder, the puzzle stops handing you enough for single candidates and single positions alone, thinning down toward twenty-seven starting digits, and that's where pointing pairs and naked pairs come in. A pointing pair is two tiles in the same box that are the only ones a digit could occupy, and if those two tiles also share a row or column, that digit can be crossed off every other tile in that row or column — because one of the pair has to take it.

A naked pair works the other way: two tiles in the same row, column or box that both have exactly the same two candidate digits left. Neither tile can be solved yet, but between them they've claimed both digits, so those two digits can be eliminated from every other tile in that group. Grid Zen never sends you a puzzle that needs more than a human solver could reasonably work out with techniques like these — every puzzle is checked in advance to make sure it's solvable without ever having to guess.

Using notes without drowning in them

Switch the input pad to the pencil and you can jot small candidate digits into a tile instead of committing to one. The useful habit is narrow, not exhaustive: note down only the two or three digits you've actually ruled everything else out for, on the specific tiles where a pointing or naked pair is close to breaking open, rather than filling every empty tile with every remaining possibility.

The game does some of the bookkeeping for you — placing a digit removes it automatically from the notes of every tile it rules out, so a well-timed note doesn't turn into stale clutter the moment the board moves on. The pad itself also tracks how many of each digit are still missing from the whole grid, and a digit disappears from the pad once all nine copies are placed, which is a fast way to see which digits are worth hunting for next.

Hearts, hints and the three stars

You get three hearts per level. Placing a wrong digit costs one, flashes red, and the tile empties again; lose all three and the level restarts. That makes hearts a reason to slow down on a tile you're not sure about rather than a punishment for being wrong — check the row, column and box highlighting again before committing, especially once you're down to your last heart.

One hint is free every level and fills in a tile of your choice, useful for breaking a genuine stall rather than for tiles you could work out with another minute of looking. Three stars needs a clean run: no wrong digits and no hint used. A one-heart-lost finish still clears the level, so treat three stars as a target for a second attempt rather than something to force on the first.

Playing on phone, tablet or keyboard

The board, tiles and digits are all drawn in 3D right in the browser, sized to hold comfortably upright on a phone, with nothing to install. Tap a tile, then a digit on the pad below; the eraser clears a tile's notes if you've changed your mind about a candidate.

On a keyboard the same actions map to arrow keys to move between tiles, 1 through 9 to enter a digit directly, N to toggle notes mode, and Backspace to clear a tile's notes — worth learning if you're solving on a desktop, since it's noticeably faster than clicking the on-screen pad for every entry.

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Play it here

• Grid Zen — Sudoku on soft 3D tiles — one answer, no guessing, three hearts