QED Logic quod erat demonstrandum

A Hard 7×7 Puzzle Solved with Forced Chain in 14 Steps

7×7 · hard · 14 steps

Play this board yourself →
A
B
C
D
E
F
G
1
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5
6
7
1×
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3×
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6×
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This 7×7 board rates as hard (difficulty score 935). Solving it from scratch takes 14 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region 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 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 row 2, so its marker has to land there; that clears every other open cell in the row.
  3. Then, every remaining candidate in this region touches E2 and F2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  4. After that, place a marker at G2. Region has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region. Placing here also clears its 2 touching neighbours.
  5. Now, 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.
  6. From there, every remaining candidate in this region touches B3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  7. Following that, if A3 were the marker, it would force F5 and F6 cleared (every open cell in row 7 belongs to the same region, so that region's marker has to be somewhere in this row), then D5 cleared (every remaining candidate in this region touches D5), then C5 cleared (every remaining candidate in this region touches C5), and the chain continues, and row 6 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 left in this region sits in row 4, so its marker has to land there; that clears every other open cell in the row.
  9. Next, 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.
  10. Then, 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.
  11. After that, place a marker at A4. Region has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region. Placing here also clears its 1 touching neighbour.
  12. Now, place a marker at B6. Region has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region.
  13. From there, 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.
  14. Finally, place a marker at F7. Region has exactly one open cell left.

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