An Expert 11×11 Puzzle Solved with Forced Chain in 28 Steps
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This 11×11 board rates as expert (difficulty score 1308). 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 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.
- Next, every remaining candidate in this region touches B10, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Then, if B1 were the marker, it would force C4 (the last open cell in region 3), then D2, H2, I2, and 2 more cleared (every open cell left in this region sits in row 2, so its marker has to land there), then E3 (the last open cell in region 4), and region 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
- After that, every remaining candidate in this region touches D2, 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 D4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- From there, marking D1 would force B2, H2, I2, and 2 more cleared (every open cell left in this region sits in row 2, so its marker has to land there), then E5, E6, E7, and 4 more cleared (every open cell left in this region sits in column E, so its marker has to land there), then B3, B4, C4, and 2 more cleared (together, two regions have open cells only in rows 3 and 4), and the chain continues, and then region 6 would be left with no open cell for its marker. So D1 can't be the marker there.
- Following that, if E1 were the marker, it would force G2 (the last open cell in region 2), then D3 (the last open cell in region 4), then B4, J4 and K4 cleared (every open cell left in this region sits in row 4, so its marker has to land there), and the chain continues, and region 6 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 F1 it would force C4, C5, C6, and 5 more cleared (every open cell left in this region sits in column C, so its marker has to land there), then B6, B7, B8, and 2 more cleared (every open cell left in this region sits in column B, so its marker has to land there), then D6, D7, D8, and 7 more cleared (together, two regions have open cells only in columns D and E), and region 9 would be left with no open cell for its marker.
- Next, marking G1 would force D3 cleared (every remaining candidate in this region touches D3), then E2, E5, E6, and 5 more cleared (every open cell left in this region sits in column E, so its marker has to land there), then C4, C5, C6, and 5 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 5 would be left with no open cell for its marker. So G1 can't be the marker there.
- Then, if H1 were the marker, it would force D3 cleared (every remaining candidate in this region touches D3), then E2, E5, E6, and 5 more cleared (every open cell left in this region sits in column E, so its marker has to land there), then C4, C5, C6, and 5 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.
- After that, that one can't be the marker: at I1 it would force D3 cleared (every remaining candidate in this region touches D3), then E2, E5, E6, and 5 more cleared (every open cell left in this region sits in column E, so its marker has to land there), then C4, C5, C6, and 5 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 be left with no open cell for its marker.
- Now, marking J1 would force D3 cleared (every remaining candidate in this region touches D3), then E2, E5, E6, and 5 more cleared (every open cell left in this region sits in column E, so its marker has to land there), then C4, C5, C6, and 5 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 5 would be left with no open cell for its marker. So J1 can't be the marker there.
- From there, if K1 were the marker, it would force D3 cleared (every remaining candidate in this region touches D3), then E2, E5, E6, and 5 more cleared (every open cell left in this region sits in column E, so its marker has to land there), then C4, C5, C6, and 5 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.
- Following that, 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.
- First, every open cell left in this region sits in row 2, 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 B, 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 3 and 4; 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, 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.
- Now, 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.
- From there, 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.
- Following that, 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 2 touching neighbours.
- 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 H6. Region has exactly one open cell left. Placing here clears the rest of row 6, column H, and its region. Placing here also clears its 1 touching neighbour.
- Then, 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.
- After that, place a marker at E7. Region has exactly one open cell left. Placing here clears the rest of row 7, column E, and its region.
- Now, place a marker at J11. Region has exactly one open cell left. Placing here clears the rest of row 11, column J, and its region.
- From there, place a marker at A9. Region has exactly one open cell left. Placing here clears the rest of row 9, column A, and its region.
- Finally, place a marker at K8. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎