QED Logic quod erat demonstrandum

An Easy 11×11 Puzzle Solved with Paired Regions in 15 Steps

11×11 · easy · 15 steps

Play this board yourself →
A
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C
D
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This 11×11 board rates as easy (difficulty score 676). Solving it from scratch takes 15 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions. Every step below is forced: nothing here is a guess.

  1. First, together, two regions have open cells only in rows 10 and 11; 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.
  2. Next, 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.
  3. Then, place a marker at C7. Region has exactly one open cell left. Placing here clears the rest of row 7, column C, and its region. Placing here also clears its 2 touching neighbours.
  4. After that, every open cell in column J 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.
  5. Now, place a marker at K9. Column 11 has exactly one open cell left. Placing here clears the rest of row 9, column K, and its region.
  6. From there, 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.
  7. Following that, place a marker at I11. Column 9 has exactly one open cell left. Placing here clears the rest of row 11, column I, and its region.
  8. First, 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.
  9. Next, 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. Placing here also clears its 2 touching neighbours.
  10. Then, place a marker at B5. Region has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
  11. After that, place a marker at E10. Region has exactly one open cell left. Placing here clears the rest of row 10, column E, and its region.
  12. Now, place a marker at F6. Region has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region.
  13. From there, place a marker at H3. Region has exactly one open cell left. Placing here clears the rest of row 3, column H, and its region. Placing here also clears its 1 touching neighbour.
  14. Following that, 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.
  15. Finally, place a marker at J2. Region has exactly one open cell left.

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