A Medium 8×8 Puzzle Solved with Forced Chain in 15 Steps
Play this board yourself →A
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This 8×8 board rates as medium (difficulty score 933). Solving it from scratch takes 15 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 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, together, two regions have open cells only in columns G and H; 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.
- After that, every remaining candidate in this region touches B3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, if C2 were the marker, it would force B5 (the last open cell in region 4), then A3 (the last open cell in region 3), then D4, E4 and F4 cleared (every open cell left in this region sits in row 4, so its marker has to land there), and the chain continues, and region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
- 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.
- Following that, 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.
- First, every open cell in row 8 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.
- Next, place a marker at C7. Row 7 has exactly one open cell left. Placing here clears the rest of row 7, column C, and its region. Placing here also clears its 2 touching neighbours.
- Then, 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 1 touching neighbour.
- After that, place a marker at B4. Region has exactly one open cell left. Placing here clears the rest of row 4, column B, and its region.
- Now, place a marker at F6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region. Placing here also clears its 1 touching neighbour.
- From there, place a marker at H5. Region has exactly one open cell left. Placing here clears the rest of row 5, column H, and its region.
- Following that, place a marker at G1. Region has exactly one open cell left.
- Finally, place a marker at E8. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎