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Shikaku: Use the Cells Shared by Every Candidate Rectangle

You do not always need to choose a complete rectangle immediately. If every legal rectangle for one clue includes a particular cell, that cell must belong to that clue's region.

PuzzleStrategy
Shikaku: Use the Cells Shared by Every Candidate Rectangle

You do not always need to choose a complete rectangle immediately. If every legal rectangle for one clue includes a particular cell, that cell must belong to that clue's region.

Compare the whole candidate set

For a clue of 6, consider all placements of 1×6, 2×3, 3×2 and 6×1 that fit the board. Each must contain that clue, contain no other clue and respect confirmed regions. Cells shared by every remaining placement are forced. Cells shared by just your two favorite options are not forced if a third legal placement avoids them.

Try the steps

  1. List every fitting size and placement for the clue.
  2. Discard candidates that break a confirmed constraint.
  3. Use their common cells to rule out conflicting candidates for neighboring clues.

Can I draw the whole border from one forced cell?

No. Ownership of a cell does not determine every edge of the rectangle. Keep uncertain boundaries open until the remaining placements agree.

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