QED Logic quod erat demonstrandum

A Medium 8×8 Puzzle Solved with Shape Squeeze in 13 Steps

8×8 · medium · 13 steps

Play this board yourself →
A
B
C
D
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F
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H
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This 8×8 board rates as medium (difficulty score 791). Solving it from scratch takes 13 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, together, two regions have open cells only in columns G and H; 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.
  2. Next, place a marker at F1. Region has exactly one open cell left. Placing here clears the rest of row 1, column F, and its region. Placing here also clears its 2 touching neighbours.
  3. Then, together, two regions have open cells only in columns E and D; 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.
  4. 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.
  5. Now, every open cell in row 2 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.
  6. From there, every remaining candidate in this region touches H4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  7. Following that, place a marker at G4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region. Placing here also clears its 1 touching neighbour.
  8. First, place a marker at C3. Row 3 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.
  9. Next, place a marker at A2. Region has exactly one open cell left. Placing here clears the rest of row 2, column A, and its region.
  10. Then, place a marker at E5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column E, and its region.
  11. After that, 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.
  12. Now, place a marker at B7. Region has exactly one open cell left. Placing here clears the rest of row 7, column B, and its region.
  13. Finally, place a marker at H6. Region has exactly one open cell left.

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