An Expert 9×9 Puzzle Solved with Forced Chain in 24 Steps
Play this board yourself →A
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This 9×9 board rates as expert (difficulty score 1202). Solving it from scratch takes 24 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region 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 1, so its marker has to land there; that clears every other open cell in the row.
- Next, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
- Then, every remaining candidate in this region touches H2 and I2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- After that, every remaining candidate in this region touches G3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, every remaining candidate in this region touches B8 and B9, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- From there, if H1 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.
- Following that, place a marker at I1. Region has exactly one open cell left. Placing here clears the rest of row 1, column I, and its region.
- First, together, two regions have open cells only in columns G and H; with one marker each, those two markers have to fill exactly those two columns, so every other region's open cells there can be cleared.
- Next, marking B2 would force H3 (the last open cell in region 2), then G8 (the last open cell in region 5), then A9 (the last open cell in region 9), and then region 7 would be left with no open cell for its marker. So B2 can't be the marker there.
- Then, if C2 were the marker, it would force H3 (the last open cell in region 2), then G8 (the last open cell in region 5), then A9 (the last open cell in region 9), and the chain continues, and row 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
- After that, that one can't be the marker: at D2 it would force H3 (the last open cell in region 2), then G8 (the last open cell in region 5), then E9 (the last open cell in region 8), and column A would be left with no open cell for its marker.
- Now, marking E2 would force H3 (the last open cell in region 2), then G8 (the last open cell in region 5), then D7 (the last open cell in region 8), and the chain continues, and then column B would be left with no open cell for its marker. So E2 can't be the marker there.
- From there, if F2 were the marker, it would force H3 (the last open cell in region 2), then G8 (the last open cell in region 5), then A9 (the last open cell in region 9), and the chain continues, and row 6 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Following that, place a marker at G2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region. Placing here also clears its 1 touching neighbour.
- First, every open cell left in this region sits in column B, so its marker has to land there; that clears every other open cell in the column.
- Next, 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.
- Then, 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.
- After that, place a marker at D7. Region has exactly one open cell left. Placing here clears the rest of row 7, column D, and its region. Placing here also clears its 2 touching neighbours.
- Now, place a marker at C9. Region has exactly one open cell left. Placing here clears the rest of row 9, column C, and its region.
- From there, every remaining candidate in this region touches E4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Following that, place a marker at F6. Region has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region. Placing here also clears its 1 touching neighbour.
- First, place a marker at E3. Region has exactly one open cell left. Placing here clears the rest of row 3, column E, and its region.
- Next, place a marker at H5. Region has exactly one open cell left. Placing here clears the rest of row 5, column H, and its region.
- Finally, place a marker at B4. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎