QED Logic quod erat demonstrandum

An Easy 10×10 Puzzle Solved with Line Confinement in 16 Steps

10×10 · easy · 16 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 easy (difficulty score 583). Solving it from scratch takes 16 logical steps, using 5 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement. Every step below is forced: nothing here is a guess.

  1. 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.
  2. Next, every open cell left in this region sits in row 10, 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 column H, so its marker has to land there; that clears every other open cell in the column.
  4. After that, place a marker at I1. Region has exactly one open cell left. Placing here clears the rest of row 1, column I, and its region. Placing here also clears its 1 touching neighbour.
  5. Now, every open cell in column A 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 open cell in column B 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.
  7. Following that, every open cell in column C 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.
  8. First, place a marker at D9. Column 4 has exactly one open cell left. Placing here clears the rest of row 9, column D, and its region. Placing here also clears its 1 touching neighbour.
  9. Next, 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.
  10. Then, 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.
  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.
  12. Now, place a marker at J7. Region has exactly one open cell left. Placing here clears the rest of row 7, column J, and its region.
  13. From there, place a marker at A4. Row 4 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.
  14. Following that, place a marker at B2. Region has exactly one open cell left. Placing here clears the rest of row 2, column B, and its region.
  15. First, 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.
  16. Finally, place a marker at F10. Region has exactly one open cell left.

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