QED Logic quod erat demonstrandum

A Steady 11×11 Puzzle Solved with Shape Squeeze in 24 Steps

11×11 · steady · 24 steps

Play this board yourself →
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This 11×11 board rates as steady (difficulty score 911). Solving it from scratch takes 24 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 1, 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 2, so its marker has to land there; that clears every other open cell in the row.
  3. Then, every remaining candidate in this region touches J2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  4. After that, 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. Placing here also clears its 3 touching neighbours.
  5. Now, place a marker at K1. Region has exactly one open cell left. Placing here clears the rest of row 1, column K, and its region.
  6. From there, together, two regions have open cells only in columns G and H; 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.
  7. Following that, every open cell left in this region sits in column J, so its marker has to land there; that clears every other open cell in the column.
  8. First, every remaining candidate in this region touches G4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  9. Next, every open cell left in this region sits in row 5, so its marker has to land there; that clears every other open cell in the row.
  10. Then, together, two regions have open cells only in rows 3 and 4; 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.
  11. After that, every remaining candidate in this region touches H4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  12. Now, place a marker at G3. Region has exactly one open cell left. Placing here clears the rest of row 3, column G, and its region. Placing here also clears its 1 touching neighbour.
  13. From there, place a marker at E4. Region has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region.
  14. Following that, place a marker at H5. Region has exactly one open cell left.
  15. First, every open cell left in this region sits in column F, so its marker has to land there; that clears every other open cell in the column.
  16. Next, 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.
  17. Then, every open cell in row 8 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
  18. After that, together, two regions have open cells only in rows 7 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.
  19. Now, 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.
  20. From there, place a marker at C9. Region has exactly one open cell left. Placing here clears the rest of row 9, column C, and its region. Placing here also clears its 2 touching neighbours.
  21. Following that, place a marker at J7. Region has exactly one open cell left.
  22. First, place a marker at A8. Region has exactly one open cell left. Placing here clears the rest of row 8, column A, and its region.
  23. Next, place a marker at B11. Region has exactly one open cell left. Placing here clears the rest of row 11, column B, and its region.
  24. Finally, place a marker at F10. Region has exactly one open cell left.

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