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Strategies for Popular Number Puzzles

Captured Candidates

Captured Candidates example
Captured Candidates example
Captured Candidates is a Cage Unit Overlap strategy but dialled down to the more obvious and easy instances that can be identified near the start. The criteria is that the cage is straight and has combinations which lead to certain numbers being necessary for that cage. The metaphor is they are "captured". We remove any others in the row, column (or box).

An example is provided on the right. 8+ in a 3-cage can be 1-2-5 or 1-3-4. Since 1 is necessary in both it can't exist elsewhere on the row.

Captured Candidates + Hidden Pairs/Triples will eliminate the same candidates as KenKen Combinations + Naked Pairs/Triples. They are two sides of the same coin. It is arbitrary which comes first but there has to be one order.

Cage Unit Overlap as used later will compute the candidates based not just on the clue and cage size but what candidates remain after other eliminations. This can be quite hard to do mentally so it is down the list.

Cage Hidden Singles

Here is an interesting situation with the yellow cage with seven cells at the bottom of the board. 'Captured Candidates' is going to find something first and call it a Cage Hidden Single. This board A to the right. This cage has seven remaining candidates spread over seven cells making it a locked set. But 4 exists only once in the cage in J4. As a 4 is necessary there being 7 for 7 in the cage, we must assume 4 is the solution for J4.

Cage Hidden Single

If this was a cage with 4 cells it would be a Naked Quad but we don't go that high for cages of size 7. Unticking 'Captured Candidates' gives us another view on the cage (B) using Cage/Unit Overlap. It identifies it as a locked set and starts to remove all other candidates that can see all of each N in the cage. The single 4 is "pointing" to all 4s it can see just as you'd expect from a single. Trace the other eliminations.

Link to example

Continue to Cage Unit Overlap


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Article created on 27-October-2026. Views: 24
This page was last modified on 27-October-2026.
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