QED Logic quod erat demonstrandum

A Medium 10×10 Puzzle Solved with Shape Squeeze in 19 Steps

10×10 · medium · 19 steps

Play this board yourself →
A
B
C
D
E
F
G
H
I
J
1
2
3
4
5
6
7
8
9
10
1×
×
×
×
×
×
×
2×
×
×
×
×
×
×
3×
×
×
×
4×
×
×
5×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
6×
×
×
×
×
×
7×
×
×
×
×
×
×
×
8×
×
×
×
×
×
9
×
×
10×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×

This 10×10 board rates as medium (difficulty score 843). Solving it from scratch takes 19 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, 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.
  2. Next, 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.
  3. Then, 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.
  4. After that, every remaining candidate in this region touches D6 and B7 and D7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  5. Now, every remaining candidate in this region touches A8 and A9, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  6. From there, place a marker at A10. Region has exactly one open cell left. Placing here clears the rest of row 10, column A, and its region. Placing here also clears its 1 touching neighbour.
  7. Following that, place a marker at B8. Region has exactly one open cell left. Placing here clears the rest of row 8, column B, and its region. Placing here also clears its 1 touching neighbour.
  8. First, place a marker at C6. Region has exactly one open cell left. Placing here clears the rest of row 6, column C, and its region. Placing here also clears its 1 touching neighbour.
  9. Next, place a marker at D9. Region has exactly one open cell left. Placing here clears the rest of row 9, column D, and its region.
  10. Then, place a marker at H7. Region has exactly one open cell left. Placing here clears the rest of row 7, column H, and its region.
  11. After that, every open cell left in this region sits in column E, so its marker has to land there; that clears every other open cell in the column.
  12. Now, every open cell left in this region sits in row 5, so its marker has to land there; that clears every other open cell in the row.
  13. From there, place a marker at E4. Region has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region. Placing here also clears its 2 touching neighbours.
  14. Following that, every open cell in column J 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.
  15. First, every remaining candidate in this region touches F2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  16. Next, place a marker at F1. Column 6 has exactly one open cell left. Placing here clears the rest of row 1, column F, and its region.
  17. Then, place a marker at J2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column J, and its region. Placing here also clears its 1 touching neighbour.
  18. After that, place a marker at G3. Region has exactly one open cell left. Placing here clears the rest of row 3, column G, and its region.
  19. Finally, place a marker at I5. Region has exactly one open cell left.

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