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 1301). Solving it from scratch takes 28 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, together, two regions have open cells only in columns J and I; with one marker each, those two markers have to fill exactly those two columns, so every other region's open cells there can be cleared.
- Next, every open cell left in this region sits in column H, so its marker has to land there; that clears every other open cell in the column.
- Then, every remaining candidate in this region touches G5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- After that, every remaining candidate in this region touches B7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, marking A1 would force B6 (the last open cell in region 7), then I8 (the last open cell in column I), then J5 (the last open cell in region 6), and the chain continues, and then row 2 would be left with no open cell for its marker. So A1 can't be the marker there.
- From there, if B1 were the marker, it would force A8, A9 and A10 cleared (every open cell left in this region sits in column A, so its marker has to land there), then D3, E3, D4, and 6 more cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), then E4, F4, E5, and 1 more cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), and the chain continues, and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Following that, that one can't be the marker: at C1 it would force D3, E3, D4, and 4 more cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), then E4, F4, E5, and 1 more cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), then F3 cleared (every remaining candidate in this region touches F3), and the chain continues, and row 4 would be left with no open cell for its marker.
- First, marking D1 would force E3, C6, C7, and 1 more cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), then E4, F4, E5, and 1 more cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), then F6, F7, F8, and 8 more cleared (together, two regions have open cells only in columns F and G), and the chain continues, and then row 2 would be left with no open cell for its marker. So D1 can't be the marker there.
- Next, every open cell in row 1 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 2 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 open cell in row 3 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.
- Now, every remaining candidate in this region touches G4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- From there, place a marker at H4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column H, and its region. Placing here also clears its 1 touching neighbour.
- Following that, place a marker at F3. Region has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region.
- First, place a marker at J5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column J, and its region.
- Next, place a marker at I8. Region has exactly one open cell left. Placing here clears the rest of row 8, column I, and its region.
- Then, together, two regions have open cells only in columns E and G; with one marker each, those two markers have to fill exactly those two columns, so every other region's open cells there can be cleared.
- After that, together, two regions have open cells only in rows 9 and 10; 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, that one can't be the marker: at A2 it would force B6 (the last open cell in region 7), then G7 (the last open cell in region 5), then E1 (the last open cell in region 2), and the chain continues, and row 10 would be left with no open cell for its marker.
- From there, marking B2 would force A9 and A10 cleared (every open cell left in this region sits in column A, so its marker has to land there), then D9 (the last open cell in region 8), and then row 10 would be left with no open cell for its marker. So B2 can't be the marker there.
- Following that, that one can't be the marker: at D2 it would force G1 (the last open cell in region 2), then E6 (the last open cell in region 5), then A7 (the last open cell in region 7), and the chain continues, and row 9 would be left with no open cell for its marker.
- First, place a marker at C2. Region has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region.
- Next, that one can't be the marker: place it at B9, and row 10 would be left with no open cell for its marker.
- 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.
- After that, 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.
- Now, place a marker at B6. Region has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region.
- From there, place a marker at G7. Region has exactly one open cell left. Placing here clears the rest of row 7, column G, and its region.
- Finally, place a marker at E1. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎