A Hard 9×9 Puzzle Solved with Forced Chain in 17 Steps
Play this board yourself →A
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This 9×9 board rates as hard (difficulty score 961). Solving it from scratch takes 17 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, 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 G, 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 H, so its marker has to land there; that clears every other open cell in the column.
- Then, every remaining candidate in this region touches G3 and I3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- After that, place a marker at G4. Region has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region. Placing here also clears its 3 touching neighbours.
- Now, 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.
- 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, 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.
- First, place a marker at D5. Region has exactly one open cell left. Placing here clears the rest of row 5, column D, 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 open cell left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
- After that, every remaining candidate in this region touches B7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, every remaining candidate in this region touches B8, 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 B6 it would force A8 (the last open cell in region 1), and column C would be left with no open cell for its marker.
- Following 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. Placing here also clears its 2 touching neighbours.
- First, place a marker at C7. Region has exactly one open cell left. Placing here clears the rest of row 7, column C, and its region.
- Next, place a marker at A6. Region has exactly one open cell left. Placing here clears the rest of row 6, column A, and its region.
- Finally, place a marker at I8. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎