An Expert 10×10 Puzzle Solved with Forced Chain in 28 Steps
Play this board yourself →A
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This 10×10 board rates as expert (difficulty score 1412). Solving it from scratch takes 28 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 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, 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.
- Then, 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.
- After that, 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.
- Now, 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.
- From there, every remaining candidate in this region touches G3 and G5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Following that, marking G4 would force I3 (the last open cell in region 4), then H7, H8, H9, and 4 more cleared (together, two regions have open cells only in columns H and J), then F10 (the last open cell in region 9), and the chain continues, and then region 7 would be left with no open cell for its marker. So G4 can't be the marker there.
- First, if H1 were the marker, it would force I3 (the last open cell in region 4), then F4 (the last open cell in region 2), then G7, G8 and G9 cleared (together, two regions have open cells only in columns J and G), 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.
- Next, marking I3 would force J1 (the last open cell in region 3), then F4 (the last open cell in region 2), then G7, G8 and G9 cleared (together, two regions have open cells only in columns H and G), and the chain continues, and then region 10 would be left with no open cell for its marker. So I3 can't be the marker there.
- Then, that one can't be the marker: at D2 it would force H3 (the last open cell in region 4), then F4 (the last open cell in region 2), then E7, G6 and G10 cleared (together, two regions have open cells only in columns E and G), and the chain continues, and region 9 would be left with no open cell for its marker.
- After that, if H4 were the marker, it would force G2 (the last open cell in region 4), then A3 (the last open cell in region 1), then I7, I8, I9, and 4 more cleared (together, two regions have open cells only in columns I and J), and the chain continues, and region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Now, place a marker at F4. Region has exactly one open cell left. Placing here clears the rest of row 4, column F, and its region. Placing here also clears its 1 touching neighbour.
- From there, that one can't be the marker: at D5 it would force G2, G6, G9, and 1 more cleared (every open cell left in this region sits in column G, so its marker has to land there), then H3 (the last open cell in region 4), then I7, I8, I9, and 4 more cleared (together, two regions have open cells only in columns I and J), and region 9 would be left with no open cell for its marker.
- Following that, marking H5 would force G2 (the last open cell in region 4), then A3 (the last open cell in region 1), then E6 (the last open cell in region 7), and the chain continues, and then column B would be left with no open cell for its marker. So H5 can't be the marker there.
- First, if I5 were the marker, it would force J1 (the last open cell in region 3), then G7, G8 and G9 cleared (together, two regions have open cells only in columns G and H), then E6 (the last open cell in region 7), and the chain continues, and column B would end up with no open cell for its marker, which can't happen. So it can't go there.
- Next, marking J1 would force A6, B6, C6, and 2 more cleared (every open cell left in this region sits in row 6, so its marker has to land there), then G2, G6, G9, and 1 more cleared (every open cell left in this region sits in column G, so its marker has to land there), then H3 (the last open cell in region 4), and the chain continues, and then region 9 would be left with no open cell for its marker. So J1 can't be the marker there.
- Then, 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.
- After that, that one can't be the marker: at A2 it would force H3 (the last open cell in region 4), then G7, G8 and G9 cleared (together, two regions have open cells only in columns J and G), then E6 (the last open cell in region 7), and the chain continues, and column G would be left with no open cell for its marker.
- Now, marking B2 would force H3 (the last open cell in region 4), then G7, G8 and G9 cleared (together, two regions have open cells only in columns J and G), then E6 (the last open cell in region 7), and the chain continues, and then column G would be left with no open cell for its marker. So B2 can't be the marker there.
- From there, if C2 were the marker, it would force H3 (the last open cell in region 4), then G7, G8 and G9 cleared (together, two regions have open cells only in columns J and G), then E6 (the last open cell in region 7), 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.
- Following that, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
- First, place a marker at G2. Region has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region.
- Next, place a marker at E6. Region has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region. Placing here also clears its 1 touching neighbour.
- Then, place a marker at D10. Region has exactly one open cell left. Placing here clears the rest of row 10, column D, and its region. Placing here also clears its 1 touching neighbour.
- After that, place a marker at C8. Region has exactly one open cell left. Placing here clears the rest of row 8, column C, and its region. Placing here also clears its 2 touching neighbours.
- Now, place a marker at B5. Region has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
- From there, place a marker at J7. Region has exactly one open cell left. Placing here clears the rest of row 7, column J, and its region.
- Finally, place a marker at H9. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎