A Sharp 11×11 Puzzle Solved with Forced Chain in 24 Steps
Play this board yourself →A
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This 11×11 board rates as sharp (difficulty score 1073). Solving it from scratch takes 24 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line 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 in row 11 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
- Then, every open cell in row 10 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
- After that, every remaining candidate in this region touches J2 and K2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Now, every remaining candidate in this region touches B3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- From there, marking J1 would force G9 (the last open cell in row 9), then E8 (the last open cell in row 8), then A10 (the last open cell in region 10), and the chain continues, and then region 3 would be left with no open cell for its marker. So J1 can't be the marker there.
- Following that, place a marker at K1. Region has exactly one open cell left. Placing here clears the rest of row 1, column K, and its region.
- First, that one can't be the marker: at A2 it would force D3 (the last open cell in region 2), and row 10 would be left with no open cell for its marker.
- Next, marking B2 would force D3 (the last open cell in region 2), then G4 (the last open cell in region 3), then A10 (the last open cell in region 10), and then region 5 would be left with no open cell for its marker. So B2 can't be the marker there.
- Then, 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.
- After that, 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 2 touching neighbours.
- Now, 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.
- From there, every open cell left in this region sits in row 7, so its marker has to land there; that clears every other open cell in the row.
- Following that, 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.
- 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, place a marker at C7. Region has exactly one open cell left. Placing here clears the rest of row 7, column C, and its region. Placing here also clears its 1 touching neighbour.
- Then, 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. Placing here also clears its 1 touching neighbour.
- After 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.
- Now, 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.
- From there, 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.
- Following that, place a marker at J9. Row 9 has exactly one open cell left. Placing here clears the rest of row 9, column J, and its region. Placing here also clears its 1 touching neighbour.
- First, place a marker at H8. Region has exactly one open cell left. Placing here clears the rest of row 8, column H, and its region.
- Next, 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.
- Finally, place a marker at I11. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎