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 1208). 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 E, so its marker has to land there; that clears every other open cell in the column.
- Then, together, two regions have open cells only in rows 8 and 9; 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.
- After that, together, two regions have open cells only in rows 6 and 7; 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.
- Now, 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.
- From there, every remaining candidate in this region touches B4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Following that, marking G1 would force F3, H3, F4, and 1 more cleared (every open cell in column I belongs to the same region, so that region's marker has to be somewhere in this column), then H4 (the last open cell in column H), then I2 (the last open cell in region 3), and the chain continues, and then column D would be left with no open cell for its marker. So G1 can't be the marker there.
- First, every remaining candidate in this region touches I2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Next, that one can't be the marker: at A2 it would force B5 and B7 cleared (every open cell left in this region sits in column B, so its marker has to land there), then C6 and C7 cleared (every open cell left in this region sits in column C, so its marker has to land there), and region 6 would be left with no open cell for its marker.
- Then, marking B2 would force A5 and A7 cleared (every open cell left in this region sits in column A, so its marker has to land there), then C6 and C7 cleared (every open cell left in this region sits in column C, so its marker has to land there), and then region 6 would be left with no open cell for its marker. So B2 can't be the marker there.
- After that, if C2 were the marker, it would force D6 (the last open cell in row 6), then F5, G5, H5, and 1 more cleared (every open cell left in this region sits in row 5, so its marker has to land there), then F4 and I4 cleared (every open cell left in this region sits in row 4, so its marker has to land there), and the chain continues, and column G would end up with no open cell for its marker, which can't happen. So it can't go there.
- Now, if F2 were the marker, it would force I1 (the last open cell in column I), then H4 (the last open cell in column H), and column G would end up with no open cell for its marker, which can't happen. So it can't go there.
- From there, that one can't be the marker: at G2 it would force I1 (the last open cell in region 2), then H4 (the last open cell in column H), then F7 (the last open cell in column F), and column D would be left with no open cell for its marker.
- Following that, 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.
- First, place a marker at F7. Region has exactly one open cell left. Placing here clears the rest of row 7, column F, and its region. Placing here also clears its 1 touching neighbour.
- Next, 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. Placing here also clears its 1 touching neighbour.
- Then, place a marker at A5. Region has exactly one open cell left. Placing here clears the rest of row 5, column A, and its region.
- After that, place a marker at E9. Region has exactly one open cell left. Placing here clears the rest of row 9, column E, and its region.
- Now, place a marker at B8. Region has exactly one open cell left.
- From there, every open cell left in this region sits in row 4, so its marker has to land there; that clears every other open cell in the row.
- Following that, every remaining candidate in this region touches H4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- First, place a marker at G4. Region has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region. Placing here also clears its 1 touching neighbour.
- Next, place a marker at I3. Region has exactly one open cell left. Placing here clears the rest of row 3, column I, and its region.
- Finally, place a marker at H1. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎