Contradiction means temporarily assuming one option for a number and following the forced consequences. If they lead to an impossible position — a number with no rectangle, or a cell nobody can cover — the assumption is false, so the other option is true.
The idea
Hard puzzles on PuzzleShikaku are graded as needing reasoning beyond forced moves, reachability and overlap. That extra step is almost always a short contradiction.
A real stuck position
This is hard 7×7 puzzle #7003 after 10 logical steps. No number is forced, no cell has a single reacher and no overlap remains. The 4 at row 3, column 7 has exactly two options:
Assume the red option. Following forced moves for 3 steps, the 3 at row 5, column 7 would have no rectangle left. That is impossible, so the red option is wrong and the 4 must be the green 1×4 rectangle. From there, ordinary techniques finish the grid.
Doing it on paper or on screen
- Choose a number with exactly two options — ideally one whose options affect many neighbours.
- Lightly mark one option (in the game, draw it; you can undo).
- Apply only certain deductions. Stop at the first impossibility.
- Undo back, and draw the other option with confidence.
Is this guessing?
No. A guess hopes; a contradiction proves. Because every puzzle here has a unique solution, one option always fails, and the failure is a logical proof. If neither option fails quickly, choose a different number.
Try this hard puzzle
Reach the stuck position yourself, then use contradiction.
Questions
Is trial and error allowed in Shikaku?
Reasoning by contradiction is a valid logical technique. Pure guessing is never needed on a well-made puzzle with a unique solution.
How do I pick which number to test?
Pick a number with exactly two options whose rectangles affect several neighbours — consequences appear faster.