A Hard 9×9 Puzzle Solved with Forced Chain in 17 Steps
Play this board yourself →A
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This 9×9 board rates as hard (difficulty score 956). Solving it from scratch takes 17 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, every open cell left in this region sits in row 9, so its marker has to land there; that clears every other open cell in the row.
- Next, together, two regions have open cells only in rows 7 and 8; 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.
- Then, every open cell left in this region sits in row 6, so its marker has to land there; that clears every other open cell in the row.
- After that, place a marker at F5. Region has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region. Placing here also clears its 2 touching neighbours.
- Now, 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. Placing here also clears its 1 touching neighbour.
- From there, place a marker at H8. Region has exactly one open cell left. Placing here clears the rest of row 8, column H, and its region.
- Following that, place a marker at A7. Region has exactly one open cell left. Placing here clears the rest of row 7, column A, and its region. Placing here also clears its 1 touching neighbour.
- First, place a marker at C6. Region has exactly one open cell left. Placing here clears the rest of row 6, column C, and its region.
- Next, if B1 were the marker, region 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Then, every open cell in row 1 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
- After that, place a marker at B9. Column 2 has exactly one open cell left. Placing here clears the rest of row 9, column B, and its region.
- Now, every remaining candidate in this region touches E3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- From there, every open cell left in this region sits in column G, so its marker has to land there; that clears every other open cell in the column.
- Following that, every remaining candidate in this region touches D2 and E2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- First, place a marker at D3. Region has exactly one open cell left. Placing here clears the rest of row 3, column D, and its region.
- Next, place a marker at E1. Region has exactly one open cell left.
- Finally, place a marker at G2. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎