QED Logic quod erat demonstrandum

A Hard 6×6 Puzzle Solved with Forced Chain in 15 Steps

6×6 · hard · 15 steps

Play this board yourself →
A
B
C
D
E
F
1
2
3
4
5
6
1×
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2
3×
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4×
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5×
6×
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This 6×6 board rates as hard (difficulty score 974). Solving it from scratch takes 15 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

  1. First, 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.
  2. Next, 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.
  3. Then, every open cell in row 4 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.
  4. After that, every remaining candidate in this region touches D1 and F1 and D2 and F2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  5. Now, 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 1 touching neighbour.
  6. From there, 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.
  7. Following that, every remaining candidate in this region touches C5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  8. First, every remaining candidate in this region touches B6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  9. Next, that one can't be the marker: at A2 it would force B5 (the last open cell in region 6), and column C would be left with no open cell for its marker.
  10. Then, place a marker at C2. Region has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region.
  11. After that, 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.
  12. Now, every remaining candidate in this region touches A5 and B5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  13. From there, 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.
  14. Following that, place a marker at B4. Region has exactly one open cell left.
  15. Finally, place a marker at D5. Region has exactly one open cell left.

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