A Hard 8×8 Puzzle Solved with Forced Chain in 15 Steps
Play this board yourself →A
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This 8×8 board rates as hard (difficulty score 963). Solving it from scratch takes 15 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 remaining candidate in this region touches F2, 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 G2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Then, 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.
- After that, together, two regions have open cells only in columns A 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, every remaining candidate in this region touches E3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- From there, that one can't be the marker: at F1 it would force D4, D5, D6, and 2 more cleared (every open cell left in this region sits in column D, so its marker has to land there), then A2, B2, C2, and 3 more cleared (together, two regions have open cells only in rows 2 and 3), then A4 (the last open cell in region 1), and the chain continues, and column B would be left with no open cell for its marker.
- Following that, place a marker at G1. Region has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region. Placing here also clears its 1 touching neighbour.
- First, place a marker at H3. Region has exactly one open cell left. Placing here clears the rest of row 3, column H, and its region.
- Next, together, two regions have open cells only in rows 2 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.
- Then, place a marker at C5. Region has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region. Placing here also clears its 2 touching neighbours.
- After that, place a marker at B2. Column 2 has exactly one open cell left. Placing here clears the rest of row 2, column B, and its region.
- Now, place a marker at F4. Region has exactly one open cell left. Placing here clears the rest of row 4, column F, and its region.
- From there, place a marker at E6. Region has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region. Placing here also clears its 1 touching neighbour.
- Following that, place a marker at D8. Region has exactly one open cell left. Placing here clears the rest of row 8, column D, and its region.
- Finally, place a marker at A7. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎