QED Logic quod erat demonstrandum

A Severe 7×7 Puzzle Solved with Forced Chain in 31 Steps

7×7 · severe · 23 steps

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A
B
C
D
E
F
G
1
2
3
4
5
6
7
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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7×
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This 7×7 board rates as severe (difficulty score 1200). Solving it from scratch takes 31 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, every open cell left in this region sits in column G, so its marker has to land there; that clears every other open cell in the column.
  3. Then, every remaining candidate in this region touches E3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  4. After that, every remaining candidate in this region touches E4 and G4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  5. Now, 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.
  6. From there, marking A1 would force C2 (the last open cell in region 2), and then region 3 would be left with no open cell for its marker. So A1 can't be the marker there.
  7. Following that, if B1 were the marker, region 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
  8. First, every open cell in row 1 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.
  9. Next, 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.
  10. Then, marking D1 would immediately leave region 3 with no open cell for its marker, so it can't be the marker there.
  11. After that, if E1 were the marker, it would force D3 (the last open cell in region 3), and region 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
  12. Now, place a marker at C1. Region has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region.
  13. From there, every open cell left in this region sits in row 7, so its marker has to land there; that clears every other open cell in the row.
  14. Following that, together, two regions have open cells only in columns A and B; 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.
  15. First, every remaining candidate in this region touches F5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  16. Next, every remaining candidate in this region touches A6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  17. Then, that one can't be the marker: at A2 it would force D3 (the last open cell in region 3), then F4 (the last open cell in region 5), and row 5 would be left with no open cell for its marker.
  18. After that, place a marker at E2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region. Placing here also clears its 1 touching neighbour.
  19. Now, place a marker at F4. Region has exactly one open cell left. Placing here clears the rest of row 4, column F, and its region. Placing here also clears its 1 touching neighbour.
  20. From there, place a marker at G6. Region has exactly one open cell left. Placing here clears the rest of row 6, column G, and its region.
  21. Following that, place a marker at D5. Region has exactly one open cell left. Placing here clears the rest of row 5, column D, and its region.
  22. First, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
  23. Finally, place a marker at B7. Region has exactly one open cell left.

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