Locked Sets: Step-by-Step Guide

Prerequisites

• Combination Pruning
• Comfort marking candidates for every run you evaluate.

How to recognize it

• Two cells share exactly two candidates (locked pair).
• Three cells share exactly three candidates, or a mix of pairs and singles that resolve into a trio.
• After pruning, the locked digits cannot appear anywhere else in the run without breaking the sum.

Step-by-step walkthrough

1. List every candidate for the run. Example: a 22-in-4 run with candidates {3,6,7,8}, {3,6,7,8}, {1,5,6,8}, {1,5,6,8}.
2. Group identical candidate sets. The first two cells share {3,6,7,8}; the latter two share {1,5,6,8}.
3. Check if the number of cells equals the number of unique digits in the group. Two cells covering {3,6,7,8} do not lock yet, but if later pruning leaves {6,8} in both spots, the pair locks those digits there.
4. Remove the locked digits from other cells in the run and update the intersecting runs accordingly.

Why it works

A Kakuro run must use each digit at most once. When two cells can only be 4 and 9, no other cell in the same run can contain those digits without creating duplicates, so the locked digits are effectively "spoken for".

Locked set variations

• Naked pairs/triples: All candidates are visible within the run. Remove them from the other cells immediately.
• Hidden pairs: Two digits appear only twice inside the combination list, even if other candidates share the cells. Highlight them to expose a locked pair.
• Pointing pairs: A locked set within an across run removes digits from the crossing down run at the shared cells.

Try it now

Create a mock 23-in-4 run where two cells already hold {4,9} and the other two hold {5,8}. Use cross sums to confirm that 4 and 9 cannot appear elsewhere. Then project those eliminations onto the intersecting runs to see the cascading effect.

Practice routine

During gameplay, pause after every major placement and scan for pairs or triples that now show up. Practising this habit for five puzzles reinforces the pattern so you spot locked sets instinctively.

Common pitfalls

• Declaring a locked set before verifying that the digits satisfy the run’s sum.
• Forgetting to remove locked digits from intersecting runs, leaving ghost candidates in place.
• Overlooking hidden pairs because extra candidates were never erased during earlier steps.

Next technique

Combine locked sets with Residual Sum Forcing to balance the remaining digits across long runs and unravel ultra hard puzzles.