Kakuro Revisited

Forced Combination (Partition Matching)

The digits of the run are known; match each one to a cell so that every cell is allowed to hold its digit.

Level 4 Combining runs Technique 10

17151011201916171032192017101191019129183981921827298192927379138
Down 20 in four cells can be 8 and 9 in the top two cells and 2 and 1 below. The candidates allow only 8 at r4c4, so the rest follow.

placed key digits removed

Why it works

Even when a run has several possible partitions, the crossing runs often leave only one way to assign the digits to the cells. That is a bipartite matching problem, and it can be solved exactly.

The app checks every assignment in polynomial time and reports the digits that every assignment keeps in a cell, and the ones no assignment uses there.

How to spot it

  1. Find the partitions that fit the remaining sum and the number of empty cells.
  2. For each partition, try to place its digits into the cells so that every cell accepts its digit.
  3. A cell that takes the same digit in every successful assignment is solved. A digit that no assignment puts in a cell can be removed there.

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.