QED Logic quod erat demonstrandum

A Sharp 6×6 Puzzle Solved with Forced Chain in 16 Steps

6×6 · sharp · 16 steps

Play this board yourself →
A
B
C
D
E
F
1
2
3
4
5
6
1×
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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 sharp (difficulty score 1044). Solving it from scratch takes 16 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, 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 F, so its marker has to land there; that clears every other open cell in the column.
  2. Next, together, two regions have open cells only in rows 5 and 6; 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.
  3. Then, every open cell in column A 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 D2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  5. Now, together, two regions have open cells only in rows 3 and 4; 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.
  6. From there, marking A1 would force E2 (the last open cell in region 2), then D4 (the last open cell in region 3), and then row 3 would be left with no open cell for its marker. So A1 can't be the marker there.
  7. Following that, place a marker at A2. Region has exactly one open cell left. Placing here clears the rest of row 2, column A, and its region.
  8. First, that one can't be the marker: at C1 it would force B4 (the last open cell in region 4), and column E would be left with no open cell for its marker.
  9. Next, together, two regions have open cells only in columns D and E; 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.
  10. Then, marking D1 would force E4 (the last open cell in region 3), then C3 (the last open cell in region 4), and then row 5 would be left with no open cell for its marker. So D1 can't be the marker there.
  11. After that, 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.
  12. Now, every remaining candidate in this region touches C3 and C4, 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 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.
  14. Following that, place a marker at D3. Region has exactly one open cell left.
  15. First, place a marker at C6. Region has exactly one open cell left. Placing here clears the rest of row 6, column C, and its region.
  16. Finally, place a marker at F5. Region has exactly one open cell left.

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