Numbridge — Strategy

Finding a cell for a digit

A beginner looks at a tile and asks: "where does this seven go?" That is the wrong question. There are usually a dozen cells on the field where a seven may stand by the rules of sudoku, and exactly one of them is right. Candidate highlighting, if the room allows it, will show you precisely that dozen — and will not help you choose at all.

Ask it the other way round: which cell knows its own digit? Find a cell with exactly one legal candidate, then look whether that digit is in your hand.

A cell with a single candidate

Hover over a cell: the table lights up its row, its slanting column and its block. Sudoku has no other constraints — everything forbidden to that cell stands in those three areas. Write down what is already there; if one option is left, the cell is solved.

in the row      1  .  3  .  5  .  7  .  9
in the column   .  2  .  4  .  .  .  8  .
in the block    .  .  .  .  .  6  .  .  .
──────────────────────────────────────────
what is left            nothing but the one digit missing

Everything from 1 to 9 is taken except one digit — so the cell knows its digit for certain. Such a move costs you nothing but attention.

A digit with a single cell

The reverse technique: take a digit from your hand and an area — a row, a column or a block — that does not contain it yet. If the whole area has only one cell where that digit could stand at all, that is where it stands. The other cells of the area are cut off by their own rows and columns.

This technique is the stronger one: it finds moves where a cell still has many candidates but a digit has no choice left.

Where to look first

Look where it is crowded: the row or the block with the most givens and closed cells gives up its digit first. An empty corner of the field almost never resolves — too little is known there.

A useful order for every turn:

1.  Is there a cell with a single candidate,
    and is that digit in my hand?        — place it, the move is free
2.  Does a digit in my hand have an area
    with only one cell left for it?      — place it
3.  Nothing deduced at all?              — see "Risk and mistakes" (5)

Three beginner mistakes

Playing by the highlight. A highlighted cell is legal, not correct: exactly one of the highlighted cells matches the solution. The highlight is a list of suspects, not a verdict.

Solving the whole field. Neither player knows the full solution, and there is no need to reconstruct it: over a game you will close barely a third of the cells. Look not for the solution but for the nearest certain move.

Forgetting that columns slant. A column drifts to the right, and the eye reads the neighbouring diagonal instead. Check yourself with the highlight: hover and make sure the cells that lit up are the ones you were counting.

Irregular blocks (jig) change none of this: a block still holds nine cells and each digit still appears once. Only the shape changes, so the areas overlap in unusual ways — which makes "one cell left for this digit" happen more often, not less.