A Severe 7×7 Puzzle Solved with Forced Chain in 22 Steps
Play this board yourself →A
B
C
D
E
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G
1
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7
1×
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2×
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3×
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×
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4🐱
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5×
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×
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6×
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7×
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This 7×7 board rates as severe (difficulty score 1273). Solving it from scratch takes 22 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region 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 row 7, so its marker has to land there; that clears every other open cell in the row.
- Next, every remaining candidate in this region touches F5 and F6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Then, every remaining candidate in this region touches B6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- After that, marking A1 would force F2 (the last open cell in column F), and then row 3 would be left with no open cell for its marker. So A1 can't be the marker there.
- Now, that one can't be the marker: at C1 it would force A2 (the last open cell in region 1), then B4 (the last open cell in region 4), and row 7 would be left with no open cell for its marker.
- From there, marking D1 would force F4 (the last open cell in column F), and then row 3 would be left with no open cell for its marker. So D1 can't be the marker there.
- Following that, if E1 were the marker, it would force F4 (the last open cell in region 3), then G6 (the last open cell in region 6), then A3 (the last open cell in row 3), and row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
- First, that one can't be the marker: at F1 it would force E4 (the last open cell in column E), and column D would be left with no open cell for its marker.
- Next, marking G1 would force F3 (the last open cell in column F), then D2 (the last open cell in column D), and then region 1 would be left with no open cell for its marker. So G1 can't be the marker there.
- Then, place a marker at B1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region. Placing here also clears its 1 touching neighbour.
- 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.
- Now, every remaining candidate in this region touches E3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- From there, every remaining candidate in this region touches F3, 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 E5, 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 D2 it would force E4 (the last open cell in region 5), and column F would be left with no open cell for its marker.
- Next, if F2 were the marker, it would force G4 (the last open cell in region 3), then E6 (the last open cell in region 6), and column D would end up with no open cell for its marker, which can't happen. So it can't go there.
- Then, place a marker at F4. Column 6 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.
- After that, place a marker at E2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region.
- Now, 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.
- 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.
- Following that, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
- Finally, place a marker at C7. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎