Sum Singles: Step-by-Step Guide

When the digits of a run are forced to a single combination, every position in that run is determined. Identifying these moments jump-starts progress and prevents you from spending time on speculative guesses.

Prerequisites

Know how Kakuro runs work and that digits 1–9 cannot repeat within a run.

How to recognize it

  • A run’s sum has only one valid combination of digits.
  • Other intersecting runs eliminate any alternative digits.

Step-by-step walkthrough

  1. Write down all digit combinations for the run. For a two-cell run totalling 15, that list is {6,9} and {7,8}.
  2. Check the crossing runs. If one intersection already forbids 6 and 9, only {7,8} remains.
  3. Place both digits, remembering that their order is decided by the other run’s requirements.
  4. Immediately re-scan the neighbouring runs; the new placements often unlock another single.

Why it works

Each Kakuro run must sum to a fixed value using unique digits. If only one combination fits that requirement, every digit in the run is forced, even if multiple cells are empty.

Sum single cheat sheet

Memorize the most common totals so you can spot singles at a glance.

Run length Target sum Forced digits
2 cells 3, 4, 16, 17 {1,2}, {1,3}, {7,9}, {8,9}
3 cells 6, 7, 23, 24 {1,2,3}, {1,2,4}, {6,8,9}, {7,8,9}
4 cells 10, 29 {1,2,3,4}, {5,7,8,9}
5 cells 15, 34 {1,2,3,4,5}, {4,6,7,8,9}

Try it now

Until the interactive trainer launches, recreate a 2×2 corner with clues 16 (across) and 4 (down). Work through which digits must fill each cell and document why any alternative fails.

Practice puzzles

Focus on easy or medium grids with many two- and three-cell runs. Challenge yourself to find every forced combination before placing other digits.

Common pitfalls

  • Forgetting that Kakuro runs cannot repeat digits—double-check before placing.
  • Overlooking intersections that could create additional sum singles.
  • Stopping after finding one forced run—systematically sweep the grid to chain multiple singles together.

Next technique

Graduate to Cross Sums for solving intersections, then explore Locked Sets when simple singles no longer crack the puzzle.