QED Logic quod erat demonstrandum

A Medium 9×9 Puzzle Solved with Shape Squeeze in 17 Steps

9×9 · medium · 17 steps

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This 9×9 board rates as medium (difficulty score 838). Solving it from scratch takes 17 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, every open cell left in this region sits in row 6, so its marker has to land there; that clears every other open cell in the row.
  2. Next, 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.
  3. Then, 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.
  4. After that, every remaining candidate in this region touches C5 and D5 and C7 and D7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  5. Now, place a marker at B7. Region has exactly one open cell left. Placing here clears the rest of row 7, column B, and its region. Placing here also clears its 3 touching neighbours.
  6. From there, place a marker at D6. Region has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region. Placing here also clears its 1 touching neighbour.
  7. Following that, place a marker at E8. Row 8 has exactly one open cell left. Placing here clears the rest of row 8, column E, and its region.
  8. First, every open cell in column I 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.
  9. Next, together, two regions have open cells only in columns A and C; 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.
  10. Then, place a marker at F3. Region has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region. Placing here also clears its 2 touching neighbours.
  11. After that, 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.
  12. Now, every remaining candidate in this region touches H2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  13. From there, 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.
  14. Following that, place a marker at I2. Region has exactly one open cell left.
  15. First, place a marker at H4. Region has exactly one open cell left. Placing here clears the rest of row 4, column H, and its region.
  16. Next, place a marker at A5. Region has exactly one open cell left. Placing here clears the rest of row 5, column A, and its region.
  17. Finally, place a marker at C9. Region has exactly one open cell left.

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