QED Logic quod erat demonstrandum

A Medium 6×6 Puzzle Solved with Shape Squeeze in 13 Steps

6×6 · medium · 13 steps

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A
B
C
D
E
F
1
2
3
4
5
6
1×
2
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3×
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4×
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5×
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6×
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This 6×6 board rates as medium (difficulty score 802). Solving it from scratch takes 13 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, 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.
  2. Next, every open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
  3. Then, 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.
  4. After that, every remaining candidate in this region touches D1 and D3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  5. Now, 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.
  6. From there, every remaining candidate in this region touches C2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  7. Following that, place a marker at D2. Region has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region. Placing here also clears its 3 touching neighbours.
  8. First, 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.
  9. Next, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
  10. Then, place a marker at F6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region. Placing here also clears its 1 touching neighbour.
  11. After that, 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.
  12. Now, 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.
  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. ∎