QED Logic quod erat demonstrandum

A Medium 11×11 Puzzle Solved with Shape Squeeze in 17 Steps

11×11 · medium · 17 steps

Play this board yourself →
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This 11×11 board rates as medium (difficulty score 807). 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 1, so its marker has to land there; that clears every other open cell in the row.
  2. Next, place a marker at F2. Region has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region. Placing here also clears its 3 touching neighbours.
  3. Then, place a marker at C3. Region has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region. Placing here also clears its 2 touching neighbours.
  4. After that, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
  5. Now, 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.
  6. From there, together, two regions have open cells only in columns A and B; 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, place a marker at E6. Region has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region. Placing here also clears its 1 touching neighbour.
  8. First, place a marker at K7. Region has exactly one open cell left. Placing here clears the rest of row 7, column K, and its region. Placing here also clears its 1 touching neighbour.
  9. Next, place a marker at J5. Region has exactly one open cell left. Placing here clears the rest of row 5, column J, and its region.
  10. Then, place a marker at A4. Region has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region.
  11. After that, 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.
  12. Now, every open cell in column G 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.
  13. From there, every remaining candidate in this region touches H9, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  14. Following that, place a marker at G9. Row 9 has exactly one open cell left. Placing here clears the rest of row 9, column G, and its region. Placing here also clears its 2 touching neighbours.
  15. First, place a marker at I8. Region has exactly one open cell left. Placing here clears the rest of row 8, column I, and its region.
  16. Next, place a marker at H1. Region has exactly one open cell left.
  17. Finally, place a marker at D10. Region has exactly one open cell left.

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