A Sharp 8×8 Puzzle Solved with Forced Chain in 27 Steps
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This 8×8 board rates as sharp (difficulty score 998). Solving it from scratch takes 27 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, 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 1 touching neighbour.
- Then, every open cell left in this region sits in row 8, so its marker has to land there; that clears every other open cell in the row.
- After that, every open cell in column A belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
- Now, every open cell in column B belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
- From there, place a marker at C3. Column 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 D1. Column 4 has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region.
- First, every remaining candidate in this region touches E6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Next, every remaining candidate in this region touches A6 and A7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Then, every remaining candidate in this region touches F7 and G7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- After that, every remaining candidate in this region touches F5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, together, two regions have open cells only in rows 6 and 7; 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.
- From there, marking A4 would force E7 (the last open cell in region 7), and then column F would be left with no open cell for its marker. So A4 can't be the marker there.
- Following that, place a marker at A5. Region has exactly one open cell left. Placing here clears the rest of row 5, column A, and its region. Placing here also clears its 1 touching neighbour.
- First, place a marker at B7. Region has exactly one open cell left. Placing here clears the rest of row 7, column B, 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.
- Then, 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.
- Finally, place a marker at E4. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎