QED Logic quod erat demonstrandum

A Steady 9×9 Puzzle Solved with Shape Squeeze in 19 Steps

9×9 · steady · 19 steps

Play this board yourself →
A
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H
I
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This 9×9 board rates as steady (difficulty score 857). Solving it from scratch takes 19 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region 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 column A, so its marker has to land there; that clears every other open cell in the column.
  2. Next, every open cell left in this region sits in column B, so its marker has to land there; that clears every other open cell in the column.
  3. Then, place a marker at C2. Region has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region. Placing here also clears its 2 touching neighbours.
  4. After that, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
  5. Now, 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.
  6. From there, every open cell left in this region sits in row 4, so its marker has to land there; that clears every other open cell in the row.
  7. Following that, together, two regions have open cells only in columns D and E; 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.
  8. First, every remaining candidate in this region touches D5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  9. Next, together, two regions have open cells only in rows 6 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.
  10. Then, place a marker at F5. Region has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region. Placing here also clears its 1 touching neighbour.
  11. After that, place a marker at D4. Region has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region.
  12. Now, place a marker at E9. Region has exactly one open cell left. Placing here clears the rest of row 9, column E, and its region.
  13. From there, place a marker at B6. Region has exactly one open cell left.
  14. Following that, every remaining candidate in this region touches G8, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  15. 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.
  16. Next, every remaining candidate in this region touches H7 and H8, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  17. Then, place a marker at G7. Region has exactly one open cell left. Placing here clears the rest of row 7, column G, and its region.
  18. After that, place a marker at H1. Region has exactly one open cell left.
  19. Finally, place a marker at I8. Region has exactly one open cell left.

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