An Expert 10×10 Puzzle Solved with Forced Chain in 29 Steps
Play this board yourself →A
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This 10×10 board rates as expert (difficulty score 1328). Solving it from scratch takes 29 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 C2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Then, every remaining candidate in this region touches C5, 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 B9, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, if B1 were the marker, it would force H2 (the last open cell in region 3), then J5, J6, J7, and 3 more cleared (every open cell left in this region sits in column J, so its marker has to land there), then E4, F4, G4, and 2 more 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 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
- From there, marking D1 would force H2 (the last open cell in region 3), then B3 (the last open cell in region 1), 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 H2 (the last open cell in region 3), then B3 (the last open cell in region 1), then J4 (the last open cell in region 4), 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 B4, B5, B6, and 3 more cleared (every open cell left in this region sits in column B, so its marker has to land there), then E4, G4, H4, and 2 more cleared (every open cell left in this region sits in row 4, so its marker has to land there), then I2, J2, H3, and 2 more cleared (together, two regions have open cells only in rows 2 and 3), and region 4 would be left with no open cell for its marker.
- Next, marking G1 would force B4, B5, B6, and 3 more cleared (every open cell left in this region sits in column B, so its marker has to land there), then E4, F4, H4, and 2 more cleared (every open cell left in this region sits in row 4, so its marker has to land there), then I2, J2, F3, and 3 more cleared (together, two regions have open cells only in rows 2 and 3), and then region 4 would be left with no open cell for its marker. So G1 can't be the marker there.
- Then, every remaining candidate in this region touches I2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- After that, if H1 were the marker, it would force B4, B5, B6, and 3 more cleared (every open cell left in this region sits in column B, so its marker has to land there), then E4, F4, G4, and 2 more cleared (every open cell left in this region sits in row 4, so its marker has to land there), then J2, F3, I3, and 1 more cleared (together, two regions have open cells only in rows 2 and 3), and region 4 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 I1 it would force B4, B5, B6, and 3 more cleared (every open cell left in this region sits in column B, so its marker has to land there), then E4, F4, G4, and 2 more cleared (every open cell left in this region sits in row 4, so its marker has to land there), then B3, C3, D3, and 3 more cleared (every open cell left in this region sits in row 3, so its marker has to land there), and the chain continues, and region 2 would be left with no open cell for its marker.
- From there, place a marker at H2. Region has exactly one open cell left. Placing here clears the rest of row 2, column H, and its region. Placing here also clears its 2 touching neighbours.
- Following that, every open cell left in this region sits in column J, so its marker has to land there; that clears every other open cell in the column.
- First, 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.
- Next, place a marker at G8. Region has exactly one open cell left. Placing here clears the rest of row 8, column G, and its region. Placing here also clears its 2 touching neighbours.
- Then, 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.
- After that, together, two regions have open cells only in columns C and B; 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, marking J1 would force B3 (the last open cell in region 1), and then column C would be left with no open cell for its marker. So J1 can't be the marker there.
- From there, 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.
- 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, together, two regions have open cells only in rows 5 and 6; 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.
- Next, 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.
- Then, 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.
- After that, place a marker at J4. Region has exactly one open cell left. Placing here also clears its 1 touching neighbour.
- Now, place a marker at I6. Region has exactly one open cell left. Placing here clears the rest of row 6, column I, and its region.
- From there, place a marker at B5. Region has exactly one open cell left.
- 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.
- Finally, place a marker at A9. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎