Rule of thumb · Puzzles and GamesNº 246 / 246

Every row, column and box of a 9 × 9 Sudoku adds to 45

What do the digits in a Sudoku row add up to?

Every row, column and box of a 9 × 9 Sudoku adds to 45, so one missing digit is 45 minus the rest.

Why it works

Each holds the digits 1 to 9 once, and 1 + 2 + … + 9 = 45. For a grid of side n it is n(n + 1)/2: 10 on 4 × 4, 21 on 6 × 6 and 136 on 16 × 16.

When it fails

It helps only when a single cell is left in a unit, and it says nothing on its own about which digit goes where. In Killer Sudoku its use is the other way round: cages that fill whole rows or boxes give away the cells left over.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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More in Puzzles and Games

← PreviousA 9 × 9 Sudoku needs at least 17 clues to have only one answer

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