QED Logic quod erat demonstrandum

A Hard 8×8 Puzzle Solved with Forced Chain in 16 Steps

8×8 · hard · 16 steps

Play this board yourself →
A
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This 8×8 board rates as hard (difficulty score 956). 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.

  1. 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.
  2. Next, 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. Placing here also clears its 1 touching neighbour.
  3. Then, 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.
  4. After that, together, two regions have open cells only in rows 3 and 4; 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.
  5. Now, every open cell in column H 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.
  6. From there, every remaining candidate in this region touches D3 and E3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  7. Following that, every open cell left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
  8. First, marking E2 would force G3 (the last open cell in region 3), then C4 (the last open cell in region 4), then F6 (the last open cell in region 5), and then column D would be left with no open cell for its marker. So E2 can't be the marker there.
  9. Next, place a marker at D2. Region has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region. Placing here also clears its 1 touching neighbour.
  10. Then, place a marker at C4. Region has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region.
  11. After that, place a marker at E5. Column 5 has exactly one open cell left. Placing here clears the rest of row 5, column E, and its region. Placing here also clears its 1 touching neighbour.
  12. Now, place a marker at F3. Column 6 has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region.
  13. From there, every remaining candidate in this region touches H6 and H7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  14. Following that, place a marker at H8. Region has exactly one open cell left. Placing here clears the rest of row 8, column H, and its region. Placing here also clears its 1 touching neighbour.
  15. First, 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.
  16. Finally, place a marker at A7. Region has exactly one open cell left.

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