QED Logic quod erat demonstrandum

A Hard 9×9 Puzzle Solved with Forced Chain in 17 Steps

9×9 · hard · 17 steps

Play this board yourself →
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This 9×9 board rates as hard (difficulty score 958). Solving it from scratch takes 17 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.

  1. First, every open cell left in this region sits in column I, so its marker has to land there; that clears every other open cell in the column.
  2. Next, place a marker at H6. Region has exactly one open cell left. Placing here clears the rest of row 6, column H, and its region. Placing here also clears its 2 touching neighbours.
  3. Then, 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.
  4. After that, together, two regions have open cells only in rows 8 and 9; 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.
  5. Now, every open cell left in this region sits in row 7, so its marker has to land there; that clears every other open cell in the row.
  6. From there, 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 2 touching neighbours.
  7. Following that, every remaining candidate in this region touches F8, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  8. First, if B1 were the marker, it would force I2 (the last open cell in region 3), then C3 (the last open cell in column C), and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
  9. Next, every remaining candidate in this region touches B3 and C3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  10. Then, 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.
  11. After that, place a marker at C1. Column 3 has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region. Placing here also clears its 1 touching neighbour.
  12. Now, place a marker at I2. Region has exactly one open cell left. Placing here clears the rest of row 2, column I, and its region.
  13. 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.
  14. 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.
  15. First, place a marker at F7. Region has exactly one open cell left. Placing here clears the rest of row 7, column F, and its region. Placing here also clears its 1 touching neighbour.
  16. Next, place a marker at G9. Region has exactly one open cell left. Placing here clears the rest of row 9, column G, and its region.
  17. Finally, place a marker at A8. Region has exactly one open cell left.

The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎