A Sharp 9×9 Puzzle Solved with Forced Chain in 29 Steps
Play this board yourself →A
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This 9×9 board rates as sharp (difficulty score 972). Solving it from scratch takes 29 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.
- First, place a marker at A8. Region has exactly one open cell left. Placing here clears the rest of row 8, column A, and its region. Placing here also clears its 2 touching neighbours.
- Next, every open cell in column I belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
- Then, every remaining candidate in this region touches H2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- After that, every remaining candidate in this region touches G2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, every open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
- From there, together, two regions have open cells only in rows 2 and 3; with one marker each, those two markers have to fill exactly those two rows, so every other region's open cells there can be cleared.
- Following that, if H1 were the marker, it would force G3 (the last open cell in region 2), then D2 (the last open cell in region 1), then C5 (the last open cell in region 6), and column B would end up with no open cell for its marker, which can't happen. So it can't go there.
- First, place a marker at G1. Region has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region. Placing here also clears its 1 touching neighbour.
- Next, place a marker at D2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region.
- Then, every open cell in column B belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
- After that, every remaining candidate in this region touches C5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, place a marker at C9. Column 3 has exactly one open cell left. Placing here clears the rest of row 9, column C, and its region.
- From there, place a marker at H7. Region has exactly one open cell left. Placing here clears the rest of row 7, column H, and its region. Placing here also clears its 1 touching neighbour.
- Following that, place a marker at F3. Region has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region. Placing here also clears its 1 touching neighbour.
- First, place a marker at E5. Region has exactly one open cell left. Placing here clears the rest of row 5, column E, and its region.
- Next, place a marker at I4. Region has exactly one open cell left. Placing here clears the rest of row 4, column I, and its region.
- Finally, place a marker at B6. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎