QED Logic quod erat demonstrandum

A Medium 10×10 Puzzle Solved with Shape Squeeze in 17 Steps

10×10 · medium · 17 steps

Play this board yourself →
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This 10×10 board rates as medium (difficulty score 812). Solving it from scratch takes 17 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region 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 2, so its marker has to land there; that clears every other open cell in the row.
  2. Next, place a marker at J3. Region has exactly one open cell left. Placing here clears the rest of row 3, column J, and its region. Placing here also clears its 1 touching neighbour.
  3. Then, 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.
  4. After that, together, two regions have open cells only in rows 1 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.
  5. Now, place a marker at G6. Region has exactly one open cell left. Placing here clears the rest of row 6, column G, and its region. Placing here also clears its 3 touching neighbours.
  6. From there, 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 1 touching neighbour.
  7. Following that, place a marker at I5. Region has exactly one open cell left. Placing here clears the rest of row 5, column I, and its region. Placing here also clears its 1 touching neighbour.
  8. First, place a marker at H1. Region has exactly one open cell left. Placing here clears the rest of row 1, column H, and its region.
  9. Next, 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.
  10. Then, 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.
  11. After that, every open cell left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
  12. Now, together, two regions have open cells only in rows 9 and 10; 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.
  13. From there, every remaining candidate in this region touches D7 and D8, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  14. Following that, place a marker at D10. Column 4 has exactly one open cell left. Placing here clears the rest of row 10, column D, and its region.
  15. First, place a marker at B9. Region has exactly one open cell left. Placing here also clears its 1 touching neighbour.
  16. Next, 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.
  17. Finally, place a marker at E8. Region has exactly one open cell left.

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