QED Logic quod erat demonstrandum

A Medium 8×8 Puzzle Solved with Shape Squeeze in 14 Steps

8×8 · medium · 14 steps

Play this board yourself →
A
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C
D
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H
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This 8×8 board rates as medium (difficulty score 805). Solving it from scratch takes 14 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, together, two regions have open cells only in rows 2 and 3; 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, 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.
  4. After that, 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. Placing here also clears its 2 touching neighbours.
  5. Now, every open cell in column D 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.
  6. From there, every remaining candidate in this region touches G2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  7. Following that, every remaining candidate in this region touches C7 and E7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  8. First, place a marker at C2. Column 3 has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region.
  9. Next, 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.
  10. Then, place a marker at H4. Region has exactly one open cell left. Placing here clears the rest of row 4, column H, and its region.
  11. After 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.
  12. Now, 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.
  13. From there, place a marker at D8. Region has exactly one open cell left. Placing here clears the rest of row 8, column D, and its region.
  14. Finally, place a marker at A7. Region has exactly one open cell left.

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