QED Logic quod erat demonstrandum

An Easy 9×9 Puzzle Solved with Shape Squeeze in 13 Steps

9×9 · easy · 13 steps

Play this board yourself →
A
B
C
D
E
F
G
H
I
1
2
3
4
5
6
7
8
9
1×
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2
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5×
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6×
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8×
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9×
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This 9×9 board rates as easy (difficulty score 780). Solving it from scratch takes 13 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, together, two regions have open cells only in columns H and I; 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.
  2. Next, place a marker at G7. Region has exactly one open cell left. Placing here clears the rest of row 7, column G, and its region. Placing here also clears its 3 touching neighbours.
  3. Then, 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 2 touching neighbours.
  4. After that, 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. Placing here also clears its 1 touching neighbour.
  5. Now, place a marker at H9. Column 8 has exactly one open cell left. Placing here clears the rest of row 9, column H, and its region.
  6. From there, place a marker at D8. Region has exactly one open cell left. Placing here clears the rest of row 8, column D, and its region.
  7. Following that, 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.
  8. First, every open cell in row 5 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, every remaining candidate in this region touches B4 and B6 and C6, 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 A6. Region has exactly one open cell left. Placing here clears the rest of row 6, column A, and its region. Placing here also clears its 1 touching neighbour.
  11. After that, 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.
  12. Now, place a marker at B2. Region has exactly one open cell left. Placing here clears the rest of row 2, column B, and its region.
  13. Finally, place a marker at I4. Region has exactly one open cell left.

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