QED Logic quod erat demonstrandum

A Medium 7×7 Puzzle Solved with Shape Squeeze in 13 Steps

7×7 · medium · 13 steps

Play this board yourself →
A
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G
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This 7×7 board rates as medium (difficulty score 794). Solving it from scratch takes 13 logical steps, using 5 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
  2. 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.
  3. Then, 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.
  4. After that, place a marker at A4. Region has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region. Placing here also clears its 1 touching neighbour.
  5. Now, 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.
  6. From there, every remaining candidate in this region touches D1 and E1 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, place a marker at F3. Region has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region. Placing here also clears its 1 touching neighbour.
  8. First, place a marker at G1. Region has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region.
  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.
  10. 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.
  11. After that, place a marker at B7. Region has exactly one open cell left. Placing here clears the rest of row 7, column B, and its region. Placing here also clears its 1 touching neighbour.
  12. Now, 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.
  13. Finally, place a marker at E6. Region has exactly one open cell left.

The key move here was Shape squeeze. Once you can spot that, this board falls quickly. ∎