QED Logic quod erat demonstrandum

A Medium 6×6 Puzzle Solved with Shape Squeeze in 14 Steps

6×6 · medium · 14 steps

Play this board yourself →
A
B
C
D
E
F
1
2
3
4
5
6
1×
2
3×
×
4×
×
×
×
×
×
×
×
×
×
5×
×
6×
×
×
×
×
×
×
×
×
×
×
×
×
×
×

This 6×6 board rates as medium (difficulty score 815). Solving it from scratch takes 14 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region 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 column B, so its marker has to land there; that clears every other open cell in the column.
  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 C, 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 rows 1 and 2; with one marker each, those two markers have to fill exactly those two rows, so every other region's open cells there can be cleared.
  5. Now, every remaining candidate in this region touches D3 and D4, 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 left in this region sits in column E, so its marker has to land there; that clears every other open cell in the column.
  7. Following that, every open cell left in this region sits in column F, so its marker has to land there; that clears every other open cell in the column.
  8. First, place a marker at C3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region. Placing here also clears its 1 touching neighbour.
  9. Next, 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.
  10. Then, place a marker at F2. Region has exactly one open cell left.
  11. After that, every remaining candidate in this region touches D5, 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 D6. Region has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region. Placing here also clears its 1 touching neighbour.
  13. From there, 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.
  14. Finally, place a marker at A5. Region has exactly one open cell left.

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