Kakuro Revisited

Cross-Run Intersection

A cell sits in two runs. When those runs allow different digits, the cell must be one the two have in common.

Level 1 Intersections Technique 04

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Across 10 in two cells allows 1, 2, 3, 4, 6, 7 and 9. Down 17 in two cells is 8 + 9, so it allows 8 and 9. Only 9 is in both lists, so r2c2 = 9.

key digits

Why it works

Each run allows a set of digits: the union of every partition that fits its remaining sum. The cell at the crossing belongs to both runs, so its digit must be in both sets.

Usually the intersection is small. When it has a single digit, the cell is solved. Even a smaller intersection is progress: every other digit can be removed.

How to spot it

  1. Take the Across run and the Down run through the cell.
  2. List the digits each run can still use, from the partitions that fit its remaining sum.
  3. The cell is one of the digits that appear in both lists.

Practice it

Open the app, choose a level that uses this technique, and ask the coach for the next step. Every hint links back to this guide.