QED Logic quod erat demonstrandum

A Medium 7×7 Puzzle Solved with Shape Squeeze in 14 Steps

7×7 · medium · 14 steps

Play this board yourself →
A
B
C
D
E
F
G
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This 7×7 board rates as medium (difficulty score 807). 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 column G, so its marker has to land there; that clears every other open cell in the column.
  2. Next, 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.
  3. Then, together, two regions have open cells only in columns D and E; 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 6 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, place a marker at C7. Row 7 has exactly one open cell left. Placing here clears the rest of row 7, column C, and its region. Placing here also clears its 1 touching neighbour.
  7. Following that, 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.
  8. First, together, two regions have open cells only in rows 1 and 2; 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.
  9. Next, every remaining candidate in this region touches E4 and G4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  10. Then, place a marker at G5. Region has exactly one open cell left. Placing here clears the rest of row 5, column G, and its region. Placing here also clears its 1 touching neighbour.
  11. After that, 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 1 touching neighbour.
  12. Now, place a marker at D4. Region has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region.
  13. From there, place a marker at E1. Region has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
  14. Finally, place a marker at B2. Region has exactly one open cell left.

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