QED Logic quod erat demonstrandum

A Medium 7×7 Puzzle Solved with Shape Squeeze in 13 Steps

7×7 · medium · 13 steps

Play this board yourself →
A
B
C
D
E
F
G
1
2
3
4
5
6
7
1×
×
×
2×
3×
×
×
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×
4×
×
×
×
×
×
×
×
×
5×
×
×
×
×
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6
×
×
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7×
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This 7×7 board rates as medium (difficulty score 795). Solving it from scratch takes 13 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 column E, so its marker has to land there; that clears every other open cell in the column.
  2. Next, together, two regions have open cells only in columns F and G; 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.
  3. Then, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
  4. After that, place a marker at C2. Region has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region. Placing here also clears its 2 touching neighbours.
  5. Now, every remaining candidate in this region touches E6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  6. From there, place a marker at E7. Region has exactly one open cell left. Placing here clears the rest of row 7, column E, and its region. Placing here also clears its 2 touching neighbours.
  7. Following that, 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.
  8. 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.
  9. Next, together, two regions have open cells only in rows 4 and 6; 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.
  10. Then, place a marker at B6. Column 2 has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region.
  11. After that, place a marker at G4. Region has exactly one open cell left. Placing here also clears its 1 touching neighbour.
  12. Now, 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.
  13. Finally, place a marker at A3. Region has exactly one open cell left.

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