QED Logic quod erat demonstrandum

A Medium 6×6 Puzzle Solved with Shape Squeeze in 15 Steps

6×6 · medium · 15 steps

Play this board yourself →
A
B
C
D
E
F
1
2
3
4
5
6
1×
×
×
2×
×
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 839). Solving it from scratch takes 15 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, 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.
  2. 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.
  3. Then, every open cell left in this region sits in column B, so its marker has to land there; that clears every other open cell in the column.
  4. After that, together, two regions have open cells only in columns C and D; 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.
  5. Now, every remaining candidate in this region touches C2 and D2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  6. From there, 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.
  7. Following that, every remaining candidate in this region touches A4 and C4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  8. First, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
  9. Next, every remaining candidate in this region touches A5, so whichever candidate ends up marked will clear it, and it 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 B4. Region has exactly one open cell left. Placing here clears the rest of row 4, column B, and its region. Placing here also clears its 1 touching neighbour.
  12. Now, place a marker at D3. Region has exactly one open cell left. Placing here clears the rest of row 3, column D, and its region. Placing here also clears its 1 touching neighbour.
  13. From there, place a marker at C1. Region has exactly one open cell left.
  14. Following that, place a marker at F2. Region has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region.
  15. Finally, place a marker at E5. Region has exactly one open cell left.

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