QED Logic quod erat demonstrandum

A Gentle 8×8 Puzzle Solved with Shape Squeeze in 13 Steps

8×8 · gentle · 13 steps

Play this board yourself →
A
B
C
D
E
F
G
H
1
2
3
4
5
6
7
8
1×
2×
×
3×
4×
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×
5×
×
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6×
×
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7
×
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8×
×
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This 8×8 board rates as gentle (difficulty score 783). Solving it from scratch takes 13 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, 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.
  2. Next, place a marker at C7. Region has exactly one open cell left. Placing here clears the rest of row 7, column C, and its region. Placing here also clears its 3 touching neighbours.
  3. 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.
  4. After that, place a marker at B1. Region has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region.
  5. Now, every open cell left in this region sits in row 2, so its marker has to land there; that clears every other open cell in the row.
  6. From there, 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.
  7. Following that, 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.
  8. First, every remaining candidate in this region touches E3 and E4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  9. Next, place a marker at F4. Region has exactly one open cell left. Placing here clears the rest of row 4, column F, and its region. Placing here also clears its 2 touching neighbours.
  10. Then, place a marker at D3. Region has exactly one open cell left.
  11. After that, place a marker at H5. Region has exactly one open cell left. Placing here clears the rest of row 5, column H, and its region.
  12. Now, place a marker at G2. Region has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region.
  13. Finally, place a marker at E8. Region has exactly one open cell left.

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