Box–Line Reduction (Claiming)

In a row or column, a digit fits only inside one box: it goes from the rest of that box.

What to look for

Pointing the other way round. Take a row (or a column) and a digit it is missing. If every cell where that digit can go lies in the same box, the line claims the digit for that box.

Why it works

The row needs the digit, and all its places are in this box. So the box’s copy of the digit is the row’s, and it cannot be in the box’s other cells: cross it out there.

Practise it

Puzzles that need it: Medium sudoku

Play this puzzle from the start

On a real puzzle

Box–line reduction

In row 3, 7 can only be in box 1.

So 7 can go from the highlighted cells.

The cells that show the pattern are in amber, the cells it changes in green, and the candidates it removes are circled.

How it works

Pick a variant and a difficulty, and play on the board: click or tap a cell, then a digit. Corner and centre marks, undo, a timer and hints are all there.

Stuck? A hint names the technique a person would use next and highlights the cells that show it.

To print, switch to Print: choose how many puzzles, which variants and difficulties, how many to a page, and where the answers go. Then print or download the PDF.

Everything runs in your browser and is free: no sign-up, nothing uploaded. Your game is saved in this browser, so you can close the page and carry on later.

What the difficulties mean

Easy: singles only (a cell with one possible digit, or a digit with one possible cell).

Medium: also pointing and box–line reductions.

Hard: also pairs, triples and quads.

Expert: also X-wings, swordfish, XY-wings, XYZ-wings and short chains.

Evil: also jellyfish and longer chains, and not just one: at least three advanced steps (fish, wings or chains) in every puzzle, except killer and consecutive ones, whose cages and bars do much of the work. Never guessing: every puzzle has exactly one solution, found by logic.

Every variant

Classic

Fill the grid so every row, column and box holds each digit once.

Killer

As classic, and the digits in each dashed cage add up to its sum, with no repeats in a cage.

Jigsaw

Every row, column and outlined shape holds each digit once.

Diagonal (X)

As classic, and both shaded diagonals hold each digit once too.

4×4 kids

Every row, column and box of four holds each symbol once.

6×6 kids

Every row, column and box of six holds each symbol once.

6×6 jigsaw

Every row, column and outlined shape of six holds each symbol once.

Even–odd

As classic; circles hold odd digits, squares even ones.

Windoku

As classic, and the four shaded boxes hold each digit once too.

Consecutive

As classic; a bar joins every pair of neighbours that differ by one, and no other pair does.

Thermo

As classic; digits rise from the bulb of each thermometer to its tip.

Arrow

As classic; the digit in each circle is the sum of the digits along its arrow (they may repeat if they don’t share a row, column or box).

Sandwich

As classic; the number outside each row and column is the sum of the digits between the 1 and the 9 in it.

16×16

Every row, column and box of sixteen holds each symbol once.

Box–line reduction

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