QED Logic quod erat demonstrandum

A Gentle 10×10 Puzzle Solved with Paired Regions in 13 Steps

10×10 · gentle · 13 steps

Play this board yourself →
A
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9
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10×
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This 10×10 board rates as gentle (difficulty score 657). Solving it from scratch takes 13 logical steps, using 5 techniques: Single cell, Row/column exclusion, Adjacency clear, Region 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 10, so its marker has to land there; that clears every other open cell in the row.
  2. Next, place a marker at B9. Region has exactly one open cell left. Placing here clears the rest of row 9, column B, and its region. Placing here also clears its 2 touching neighbours.
  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, place a marker at A1. Region has exactly one open cell left. Placing here clears the rest of row 1, column A, and its region.
  5. Now, 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.
  6. From there, place a marker at F3. Region has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region. Placing here also clears its 2 touching neighbours.
  7. Following that, 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.
  8. First, place a marker at D4. Column 4 has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region.
  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. Placing here also clears its 1 touching neighbour.
  10. Then, 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.
  11. After that, place a marker at H8. Region has exactly one open cell left. Placing here clears the rest of row 8, column H, and its region.
  12. Now, place a marker at G10. Region has exactly one open cell left. Placing here clears the rest of row 10, column G, and its region.
  13. Finally, place a marker at E6. Region has exactly one open cell left.

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