An Expert 10×10 Puzzle Solved with Forced Chain in 23 Steps
Play this board yourself →A
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This 10×10 board rates as expert (difficulty score 1237). Solving it from scratch takes 23 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, 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.
- Next, place a marker at F8. Region has exactly one open cell left. Placing here clears the rest of row 8, column F, and its region. Placing here also clears its 3 touching neighbours.
- Then, place a marker at G10. Region has exactly one open cell left. Placing here clears the rest of row 10, column G, and its region.
- After that, place a marker at B9. Region has exactly one open cell left. Placing here clears the rest of row 9, column B, and its region.
- Now, 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.
- From there, every remaining candidate in this region touches H6 and I6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Following that, marking A1 would force I2 (the last open cell in region 4), and then region 3 would be left with no open cell for its marker. So A1 can't be the marker there.
- First, that one can't be the marker: at C1 it would force I2 (the last open cell in region 4), and region 3 would be left with no open cell for its marker.
- Next, marking D1 would force I2 (the last open cell in region 4), and then region 3 would be left with no open cell for its marker. So D1 can't be the marker there.
- Then, if H1 were the marker, region 3 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 J2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, that one can't be the marker: at I1 it would force H3 (the last open cell in region 3), and row 7 would be left with no open cell for its marker.
- From there, marking J1 would force H4, H5 and H7 cleared (every open cell left in this region sits in column H, so its marker has to land there), then I7 (the last open cell in region 7), and then region 5 would be left with no open cell for its marker. So J1 can't be the marker there.
- Following that, place a marker at I2. Region has exactly one open cell left. Placing here clears the rest of row 2, column I, and its region. Placing here also clears its 2 touching neighbours.
- First, place a marker at E1. Region has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
- Next, place a marker at H7. Region has exactly one open cell left. Placing here clears the rest of row 7, column H, and its region.
- Then, every remaining candidate in this region touches C4 and D4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- After that, if A3 were the marker, it would force D5 (the last open cell in region 2), and column C would end up with no open cell for its marker, which can't happen. So it can't go there.
- Now, if D3 were the marker, region 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
- From there, place a marker at C3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region.
- Following that, place a marker at A4. Region has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region.
- First, place a marker at D6. Region has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region.
- Finally, place a marker at J5. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎