A Hard 9×9 Puzzle Solved with Forced Chain in 16 Steps
Play this board yourself →A
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This 9×9 board rates as hard (difficulty score 966). Solving it from scratch takes 16 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 D, so its marker has to land there; that clears every other open cell in the column.
- Next, every open cell left in this region sits in column E, so its marker has to land there; that clears every other open cell in the column.
- Then, together, two regions have open cells only in rows 1 and 2; 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, place a marker at E3. Region has exactly one open cell left. Placing here clears the rest of row 3, column E, and its region. Placing here also clears its 3 touching neighbours.
- Now, place a marker at D1. Region has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region.
- From there, place a marker at G2. Region has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region.
- Following that, place a marker at C4. Region has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region. Placing here also clears its 1 touching neighbour.
- First, place a marker at I5. Region has exactly one open cell left. Placing here clears the rest of row 5, column I, and its region. Placing here also clears its 1 touching neighbour.
- Next, 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.
- Then, every remaining candidate in this region touches B6 and B7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- After that, marking F6 would force A7 (the last open cell in region 7), and then row 8 would be left with no open cell for its marker. So F6 can't be the marker there.
- Now, place a marker at A6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column A, and its region.
- From there, that one can't be the marker: place it at F7, and column H would be left with no open cell for its marker.
- Following that, place a marker at H7. Row 7 has exactly one open cell left. Placing here clears the rest of row 7, column H, and its region.
- First, place a marker at F9. Region has exactly one open cell left. Placing here clears the rest of row 9, column F, and its region.
- Finally, place a marker at B8. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎