QED Logic quod erat demonstrandum

An Easy 10×10 Puzzle Solved with Line Confinement in 14 Steps

10×10 · easy · 14 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×
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2×
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3×
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4×
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5×
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6×
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7×
8×
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9
×
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10×
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This 10×10 board rates as easy (difficulty score 562). Solving it from scratch takes 14 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 column J, 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 open cell in row 10 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.
  4. After that, every open cell in row 9 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.
  5. Now, place a marker at C8. Row 8 has exactly one open cell left. Placing here clears the rest of row 8, column C, and its region. Placing here also clears its 2 touching neighbours.
  6. From there, place a marker at B6. Region has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region. Placing here also clears its 2 touching neighbours.
  7. Following 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.
  8. First, place a marker at I5. Region has exactly one open cell left. Placing here clears the rest of row 5, column I, and its region.
  9. Next, place a marker at E7. Region has exactly one open cell left. Placing here clears the rest of row 7, column E, and its region.
  10. Then, place a marker at G9. Region has exactly one open cell left. Placing here clears the rest of row 9, column G, and its region. Placing here also clears its 2 touching neighbours.
  11. After that, place a marker at D10. Region has exactly one open cell left. Placing here clears the rest of row 10, column D, and its region.
  12. Now, place a marker at F1. Region has exactly one open cell left. Placing here clears the rest of row 1, column F, and its region.
  13. From there, place a marker at J2. Region has exactly one open cell left. Placing here clears the rest of row 2, column J, and its region.
  14. Finally, place a marker at H3. Region has exactly one open cell left.

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