A Hard 8×8 Puzzle Solved with Forced Chain in 17 Steps
Play this board yourself →A
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This 8×8 board rates as hard (difficulty score 1006). Solving it from scratch takes 17 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 row 1, so its marker has to land there; that clears every other open cell in the row.
- Next, place a marker at A2. Region has exactly one open cell left. Placing here clears the rest of row 2, column A, and its region. Placing here also clears its 1 touching neighbour.
- Then, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
- After that, every remaining candidate in this region touches B5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, marking G1 would force D4, E4, F4, and 2 more cleared (together, two regions have open cells only in rows 4 and 5), then D6 (the last open cell in region 5), then E8 (the last open cell in column E), and the chain continues, and then row 4 would be left with no open cell for its marker. So G1 can't be the marker there.
- From there, place a marker at F1. Region has exactly one open cell left. Placing here clears the rest of row 1, column F, and its region.
- Following that, 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.
- First, marking C3 would immediately leave region 4 with no open cell for its marker, so it can't be the marker there.
- Next, 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. Placing here also clears its 1 touching neighbour.
- Then, together, two regions have open cells only in rows 4 and 5; 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.
- After that, every open cell left in this region sits in column G, so its marker has to land there; that clears every other open cell in the column.
- Now, place a marker at E5. Region has exactly one open cell left. Placing here clears the rest of row 5, column E, and its region.
- From there, place a marker at B4. Region has exactly one open cell left. Placing here clears the rest of row 4, column B, and its region.
- Following that, every remaining candidate in this region touches H6 and H7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- First, place a marker at H8. Region has exactly one open cell left. Placing here clears the rest of row 8, column H, and its region. Placing here also clears its 1 touching neighbour.
- Next, place a marker at G6. Region has exactly one open cell left. Placing here clears the rest of row 6, column G, and its region.
- Finally, place a marker at C7. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎