An Expert 10×10 Puzzle Solved with Forced Chain in 22 Steps
Play this board yourself →A
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This 10×10 board rates as expert (difficulty score 1221). Solving it from scratch takes 22 logical steps, using 5 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Forced chain. Every step below is forced: nothing here is a guess.
- First, marking A1 would force C2, F2, G2, and 3 more cleared (every open cell left in this region sits in row 2, so its marker has to land there), then B3, B4 and B7 cleared (every open cell left in this region sits in column B, so its marker has to land there), then C3 (the last open cell in region 3), and the chain continues, and then region 4 would be left with no open cell for its marker. So A1 can't be the marker there.
- Next, if B1 were the marker, it would force F2, G2, H2, and 2 more cleared (every open cell left in this region sits in row 2, so its marker has to land there), then A4 and A5 cleared (every open cell left in this region sits in column A, so its marker has to land there), then C3 (the last open cell in region 3), and the chain continues, and region 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Then, marking D1 would immediately leave region 2 with no open cell for its marker, so it can't be the marker there.
- After that, if E1 were the marker, it would force I3, H5, I5, and 4 more cleared (every open cell in column J belongs to the same region, so that region's marker has to be somewhere in this column), then A4, A5, B3, and 2 more cleared (together, two regions have open cells only in columns A and B), then C4, C5, C6, and 4 more cleared (every open cell left in this region sits in column C, so its marker has to land there), and the chain continues, and region 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Now, that one can't be the marker: at F1 it would force I3, H5, I5, and 4 more cleared (every open cell in column J belongs to the same region, so that region's marker has to be somewhere in this column), then A4, A5, B3, and 2 more cleared (together, two regions have open cells only in columns A and B), then C4, C5, C6, and 4 more cleared (every open cell left in this region sits in column C, so its marker has to land there), and the chain continues, and region 4 would be left with no open cell for its marker.
- From there, marking G1 would force I3, H5, I5, and 4 more cleared (every open cell in column J belongs to the same region, so that region's marker has to be somewhere in this column), then A4, A5, B3, and 2 more cleared (together, two regions have open cells only in columns A and B), then C4, C5, C6, and 4 more cleared (every open cell left in this region sits in column C, so its marker has to land there), and the chain continues, and then region 4 would be left with no open cell for its marker. So G1 can't be the marker there.
- Following that, if H1 were the marker, it would force I3, I5, I6, and 2 more cleared (every open cell in column J belongs to the same region, so that region's marker has to be somewhere in this column), then A4, A5, B3, and 2 more cleared (together, two regions have open cells only in columns A and B), then C4, C5, C6, and 4 more cleared (every open cell left in this region sits in column C, so its marker has to land there), and the chain continues, and region 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
- First, that one can't be the marker: at I1 it would force H5 and H6 cleared (every open cell in column J belongs to the same region, so that region's marker has to be somewhere in this column), then A4, A5, B3, and 2 more cleared (together, two regions have open cells only in columns A and B), then C4, C5, C6, and 4 more cleared (every open cell left in this region sits in column C, so its marker has to land there), and the chain continues, and region 4 would be left with no open cell for its marker.
- Next, marking J1 would force A4, A5, B3, and 2 more cleared (together, two regions have open cells only in columns A and B), then C4, C5, C6, and 4 more cleared (every open cell left in this region sits in column C, so its marker has to land there), then F2, G2, H2, and 6 more cleared (together, two regions have open cells only in rows 2 and 3), and the chain continues, and then region 4 would be left with no open cell for its marker. So J1 can't be the marker there.
- Then, place a marker at C1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region. Placing here also clears its 1 touching neighbour.
- After that, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region. Placing here also clears its 2 touching neighbours.
- Now, place a marker at D4. Region has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region.
- From there, place a marker at F10. Region has exactly one open cell left. Placing here clears the rest of row 10, column F, and its region. Placing here also clears its 1 touching neighbour.
- Following that, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
- First, 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. Placing here also clears its 1 touching neighbour.
- Next, 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.
- Then, place a marker at G6. Region has exactly one open cell left. Placing here clears the rest of row 6, column G, and its region. Placing here also clears its 1 touching neighbour.
- After that, place a marker at H3. Region has exactly one open cell left. Placing here clears the rest of row 3, column H, and its region.
- Now, every open cell left in this region sits in column I, so its marker has to land there; that clears every other open cell in the column.
- From there, place a marker at J7. Row 7 has exactly one open cell left. Placing here clears the rest of row 7, column J, and its region. Placing here also clears its 1 touching neighbour.
- Following that, place a marker at I9. Region has exactly one open cell left. Placing here clears the rest of row 9, column I, and its region.
- Finally, place a marker at B8. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎