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
2
3
4
5
6
7
1×
×
×
×
×
×
2
×
3×
×
4×
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×
×
×
×
×
×
×
5
×
×
6×
×
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7×
×
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This 7×7 board rates as medium (difficulty score 827). Solving it from scratch takes 14 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Line confinement, Paired regions, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, 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. Placing here also clears its 1 touching neighbour.
  2. Next, every open cell in column F belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
  3. Then, every open cell in column E belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
  4. After 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.
  5. Now, together, two regions have open cells only in columns A and B; 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.
  6. From there, every remaining candidate in this region touches D4 and F4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  7. Following that, every remaining candidate in this region touches C6 and D6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  8. First, place a marker at D7. Region has exactly one open cell left. Placing here clears the rest of row 7, column D, and its region.
  9. Next, place a marker at C5. Region has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region. Placing here also clears its 1 touching neighbour.
  10. Then, place a marker at B2. Column 2 has exactly one open cell left. Placing here clears the rest of row 2, column B, and its region.
  11. After that, every remaining candidate in this region touches F3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  12. Now, place a marker at F6. Region has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region.
  13. From there, place a marker at A4. Region has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region.
  14. Finally, place a marker at E3. Region has exactly one open cell left.

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