A Hard 7×7 Puzzle Solved with Forced Chain in 16 Steps
Play this board yourself →A
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This 7×7 board rates as hard (difficulty score 973). Solving it from scratch takes 16 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.
- First, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
- Next, 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.
- Then, together, two regions have open cells only in rows 1 and 2; 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.
- After that, place a marker at B3. Region has exactly one open cell left. Placing here clears the rest of row 3, column B, and its region. Placing here also clears its 2 touching neighbours.
- Now, place a marker at A1. Region has exactly one open cell left. Placing here clears the rest of row 1, column A, and its region.
- From there, every remaining candidate in this region touches E4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Following that, every remaining candidate in this region touches D5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- First, that one can't be the marker: at G2 it would force C6 cleared (every open cell left in this region sits in row 6, so its marker has to land there), then E5 and E7 cleared (every remaining candidate in this region touches E5 and E7), then E6 (the last open cell in column E), and the chain continues, and column D would be left with no open cell for its marker.
- Next, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region.
- Then, 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.
- After that, every open cell in column G 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.
- Now, every remaining candidate in this region touches G4 and G5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- 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. Placing here also clears its 1 touching neighbour.
- Following that, 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.
- First, place a marker at C5. Region has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region.
- Finally, place a marker at D7. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎