QED Logic quod erat demonstrandum

A Sharp 7×7 Puzzle Solved with Forced Chain in 17 Steps

7×7 · sharp · 17 steps

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A
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D
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G
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7×
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This 7×7 board rates as sharp (difficulty score 1048). Solving it from scratch takes 17 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.

  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, 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.
  3. Then, every remaining candidate in this region touches A4 and C4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  4. After that, place a marker at A5. Region has exactly one open cell left. Placing here clears the rest of row 5, column A, and its region. Placing here also clears its 1 touching neighbour.
  5. Now, 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 1 touching neighbour.
  6. From there, if E1 were the marker, row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
  7. Following that, that one can't be the marker: at F1 it would force D2 (the last open cell in row 2), then C6 (the last open cell in region 4), and region 7 would be left with no open cell for its marker.
  8. First, marking G1 would force C6 (the last open cell in column C), and then region 7 would be left with no open cell for its marker. So G1 can't be the marker there.
  9. 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.
  10. Then, every open cell in row 1 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.
  11. After that, that one can't be the marker: at G2 it would force C1 (the last open cell in column C), then F7 (the last open cell in region 5), and column E would be left with no open cell for its marker.
  12. Now, 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.
  13. From there, 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.
  14. Following that, place a marker at E6. Column 5 has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region.
  15. First, place a marker at D4. Region has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region.
  16. Next, place a marker at C1. Region has exactly one open cell left.
  17. Finally, place a marker at G7. Region has exactly one open cell left.

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