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
1
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5
6
7
1×
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4
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7
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This 7×7 board rates as medium (difficulty score 813). 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 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.
  2. Next, every remaining candidate in this region touches F5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  3. Then, 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.
  4. After that, together, two regions have open cells only in columns E and F; 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.
  5. Now, place a marker at D6. Region has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region. Placing here also clears its 3 touching neighbours.
  6. From there, 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.
  7. Following that, 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.
  8. First, every open cell in row 1 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.
  9. Next, 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.
  10. Then, 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.
  11. After that, 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.
  12. Now, place a marker at G5. Region has exactly one open cell left. Placing here also clears its 1 touching neighbour.
  13. From there, place a marker at E4. Region has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region.
  14. Finally, place a marker at F1. Region has exactly one open cell left.

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