QED Logic quod erat demonstrandum

A Gentle 7×7 Puzzle Solved with Paired Regions in 10 Steps

7×7 · gentle · 10 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 gentle (difficulty score 652). Solving it from scratch takes 10 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions. Every step below is forced: nothing here is a guess.

  1. First, 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.
  2. Next, 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. Placing here also clears its 1 touching neighbour.
  3. Then, together, two regions have open cells only in rows 4 and 5; 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.
  4. After that, every open cell in column B 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.
  5. Now, place a marker at C3. Column 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 2 touching neighbours.
  6. From there, place a marker at B1. Region has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region.
  7. Following 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.
  8. First, 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.
  9. Next, 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.
  10. Finally, place a marker at E7. Region has exactly one open cell left.

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