Cross Sums
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Strategy

Cross Sums Solving Tips & Strategy

A practical guide to solving cross sums faster: learn the sums with only one possible set of digits, start from short runs, use intersections, and keep clean pencil notes.

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The core idea

Solve where the options are fewest

Cross sums is a puzzle of elimination. Short runs and extreme sums allow very few digit combinations, so they anchor the grid. Every digit you place shrinks the options in the crossing run, which is how a blank-looking grid suddenly opens up.

  • 01

    Start with the two-cell runs. Clues of 3, 4, 16 and 17 have only one possible pair of digits.

  • 02

    Memorise the unique combinations for longer runs too: 6 and 7 in three cells, 10 and 11 in four, 23 and 24 at the top end.

  • 03

    Look for crossings between two runs whose candidate digits share only one value; that cell is forced.

  • 04

    If a two-cell run must be 1 and 2, any crossing run that already contains a 1 or a 2 elsewhere tells you which way round they go.

  • 05

    Use pencil notes early. Writing the possible digits in each cell makes forced cells and eliminations visible.

  • 06

    A long run with a very high or very low sum is nearly complete before you start. Fill it first.

  • 07

    If you are stuck, hunt for a run where all but one cell is filled — the last digit is just subtraction.

Cheat sheet

Sums with only one set of digits

For these run lengths and totals there is exactly one group of digits that works. You still have to work out the order, but you know which digits to pencil in. Runs of eight cells have a unique set for every total, and a nine-cell run is always 1 to 9 (45).

Unique digit combinations by run length and sum
Cells in runSum → digits
2
  • 3 → 1 2
  • 4 → 1 3
  • 16 → 7 9
  • 17 → 8 9
3
  • 6 → 1 2 3
  • 7 → 1 2 4
  • 23 → 6 8 9
  • 24 → 7 8 9
4
  • 10 → 1 2 3 4
  • 11 → 1 2 3 5
  • 29 → 5 7 8 9
  • 30 → 6 7 8 9
5
  • 15 → 1 2 3 4 5
  • 16 → 1 2 3 4 6
  • 34 → 4 6 7 8 9
  • 35 → 5 6 7 8 9
6
  • 21 → 1 2 3 4 5 6
  • 22 → 1 2 3 4 5 7
  • 38 → 3 5 6 7 8 9
  • 39 → 4 5 6 7 8 9

Avoid these

Common mistakes

  • Repeating a digit in a run

    The most common slip. If a run of four needs to total 10, it must be 1, 2, 3 and 4 — you cannot use 2 twice to make the sum. The board marks duplicates in red the moment they appear.

  • Guessing instead of eliminating

    Every puzzle has a logical route from start to finish. If two digits both seem to fit, note both and look at the crossing runs instead of picking one.

  • Ignoring the crossing run

    A digit that fits the across sum may be impossible for the down sum. Always check both clues before committing.

  • Forgetting to clear notes

    Old pencil marks that no longer apply cause false deductions. This game clears a placed digit from the notes of every cell in its runs, but notes you typed for other reasons are yours to maintain.

New to the rules? Read the how-to-play guide or jump straight in.

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