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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This 8×8 board rates as medium (difficulty score 791). Solving it from scratch takes 14 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, together, two regions have open cells only in rows 1 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 remaining candidate in this region touches F2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  4. After that, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region. Placing here also clears its 3 touching neighbours.
  5. Now, every open cell left in this region sits in column G, so its marker has to land there; that clears every other open cell in the column.
  6. From there, 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. Placing here also clears its 1 touching neighbour.
  7. Following 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.
  8. First, 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.
  9. Next, place a marker at D5. Region has exactly one open cell left. Placing here clears the rest of row 5, column D, and its region.
  10. Then, every open cell left in this region sits in column A, 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 F, so its marker has to land there; that clears every other open cell in the column.
  12. Now, place a marker at B8. Row 8 has exactly one open cell left. Placing here clears the rest of row 8, column B, and its region. Placing here also clears its 1 touching neighbour.
  13. From there, place a marker at A6. Region has exactly one open cell left. Placing here clears the rest of row 6, column A, and its region.
  14. Finally, place a marker at F7. Region has exactly one open cell left.

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