QED Logic quod erat demonstrandum

An Easy 10×10 Puzzle Solved with Paired Regions in 15 Steps

10×10 · easy · 15 steps

Play this board yourself →
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This 10×10 board rates as easy (difficulty score 680). 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, 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.
  2. Next, every open cell in row 1 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.
  3. Then, place a marker at F2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region. Placing here also clears its 2 touching neighbours.
  4. After that, place a marker at G5. Region has exactly one open cell left. Placing here clears the rest of row 5, column G, and its region. Placing here also clears its 1 touching neighbour.
  5. Now, place a marker at H7. Region has exactly one open cell left. Placing here clears the rest of row 7, column H, and its region. Placing here also clears its 2 touching neighbours.
  6. From there, 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.
  7. Following that, every open cell in row 3 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.
  8. First, 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.
  9. Next, 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 1 touching neighbour.
  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 B6. Region has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region.
  12. Now, place a marker at J8. Region has exactly one open cell left. Placing here clears the rest of row 8, column J, and its region. Placing here also clears its 1 touching neighbour.
  13. From there, place a marker at I10. Region has exactly one open cell left. Placing here clears the rest of row 10, column I, and its region.
  14. Following that, place a marker at D1. Region has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region.
  15. Finally, place a marker at E9. Region has exactly one open cell left.

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