QED Logic quod erat demonstrandum

A Medium 7×7 Puzzle Solved with Forced Chain in 12 Steps

7×7 · medium · 12 steps

Play this board yourself →
A
B
C
D
E
F
G
1
2
3
4
5
6
7
1×
×
×
2×
3
×
4×
×
×
×
×
×
×
5×
×
×
×
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×
×
×
×
×
×
6×
×
7
×
×
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This 7×7 board rates as medium (difficulty score 899). Solving it from scratch takes 12 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Paired regions, 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 column B, 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 row 2, so its marker has to land there; that clears every other open cell in the row.
  4. After that, together, two regions have open cells only in columns A and C; 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.
  5. Now, place a marker at D3. Region has exactly one open cell left. Placing here clears the rest of row 3, column D, and its region. Placing here also clears its 2 touching neighbours.
  6. From there, 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.
  7. Following that, place a marker at C7. Region has exactly one open cell left. Placing here clears the rest of row 7, column C, and its region. Placing here also clears its 1 touching neighbour.
  8. First, place a marker at B5. Region has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
  9. Next, that one can't be the marker: at F1 it would force G6 (the last open cell in region 6), and row 4 would be left with no open cell for its marker.
  10. Then, 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.
  11. After that, place a marker at G4. Region has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region.
  12. Finally, place a marker at F6. Region has exactly one open cell left.

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