A Medium 7×7 Puzzle Solved with Forced Chain in 13 Steps
Play this board yourself →A
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This 7×7 board rates as medium (difficulty score 917). Solving it from scratch takes 13 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.
- 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.
- 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.
- Then, every remaining candidate in this region touches E2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- After that, place a marker at F2. Region has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region. Placing here also clears its 3 touching neighbours.
- Now, place a marker at D1. Region has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region.
- From there, place a marker at E4. Region has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region.
- Following that, every open cell in row 3 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.
- First, if A3 were the marker, it would force G6 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 C6 cleared (every remaining candidate in this region touches C6), then G5 (the last open cell in region 5), and the chain continues, and row 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Next, 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.
- Then, place a marker at G5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column G, and its region.
- After that, place a marker at A6. Row 6 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.
- Now, 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.
- Finally, place a marker at B3. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎