An Expert 10×10 Puzzle Solved with Forced Chain in 24 Steps
Play this board yourself →A
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This 10×10 board rates as expert (difficulty score 1229). 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 column A, so its marker has to land there; that clears every other open cell in the column.
- Next, together, two regions have open cells only in columns B and C; 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.
- Then, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
- After that, together, two regions have open cells only in columns E and F; 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.
- Now, every remaining candidate in this region touches E8, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- From there, marking G1 would force E2 (the last open cell in region 1), then H4, I4, J4, and 5 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 then row 4 would be left with no open cell for its marker. So G1 can't be the marker there.
- Following that, that one can't be the marker: at I1 it would force E2 (the last open cell in region 1), then H4, J4, J5, and 3 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 G4 (the last open cell in row 4), and the chain continues, and column A would be left with no open cell for its marker.
- First, marking J1 would force E2 (the last open cell in region 1), then H4, I4 and I6 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 G4 (the last open cell in row 4), and the chain continues, and then column A would be left with no open cell for its marker. So J1 can't be the marker there.
- Next, that one can't be the marker: at G2 it would force E1 (the last open cell in region 1), then H4, I4, J4, and 5 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 row 4 would be left with no open cell for its marker.
- Then, marking H2 would immediately leave row 3 with no open cell for its marker, so it can't be the marker there.
- After that, if I2 were the marker, it would force G3 (the last open cell in region 2), and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Now, if E1 were the marker, it would force J2 (the last open cell in row 2), then H3 (the last open cell in row 3), and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
- From there, that one can't be the marker: at F1 it would force J2 (the last open cell in row 2), then H3 (the last open cell in row 3), and row 4 would be left with no open cell for its marker.
- Following 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.
- First, place a marker at H1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column H, and its region.
- Next, 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.
- Then, place a marker at G4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region.
- After that, place a marker at B5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
- Now, 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.
- From there, place a marker at D9. Region has exactly one open cell left. Placing here clears the rest of row 9, column D, and its region.
- Following that, place a marker at A10. Region has exactly one open cell left. Placing here clears the rest of row 10, column A, and its region.
- First, 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.
- Next, place a marker at J3. Region has exactly one open cell left.
- Finally, place a marker at F6. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎