Find the Cat #219: 10x10 Grid Puzzle (Hard)

hard

Tap a square: ✕ (ruled out) → 🐱 (cat) → clear

0 / 10 cats · 0:00
Red (8)Orange (20)Yellow (1)Green (10)Teal (12)Blue (12)Purple (3)Pink (7)Brown (15)Grey (12)

Can you place all 10 cats? One per row, one per column, one per color -- and keep them at least one square apart in every direction.

  • One cat in every row and every column.
  • One cat in every color region.
  • Cats can’t touch — not even diagonally.

Step-by-step solution

Squares are written as R<row>C<column>, counting from the top-left. Cross out the squares listed, and place a cat wherever a step says so.

  1. The Yellow region has only one open square left: R9C3. Put a cat there.
  2. Wherever the cat in the Purple region ends up, it rules out R2C9. Cross that square out.
  3. Wherever the cat in the Grey region ends up, it rules out R7C1. Cross that square out.
  4. The Teal and Pink regions can only use columns 1 and 2, so columns 1 and 2 are already spoken for. Cross out R6C2 and R7C2.
  5. The Grey region has only one open square left: R7C4. Put a cat there.
  6. Wherever the cat in the Red region ends up, it rules out R1C1, R1C2, R1C7, R1C8, R1C9, R1C10 and 2 more. Cross those squares out.
  7. The Purple region has only one open square left: R2C10. Put a cat there.
  8. The Pink region has only one open square left: R3C1. Put a cat there.
  9. The Teal region has only one open square left: R5C2. Put a cat there.
  10. Wherever the cat in the Orange region ends up, it rules out R4C9. Cross that square out.
  11. Wherever the cat in the Green region ends up, it rules out R10C6. Cross that square out.
  12. The Red and Green regions can only use columns 5 and 6, so columns 5 and 6 are already spoken for. Cross out R4C5, R4C6 and R6C6.
  13. Wherever the cat in the Brown region ends up, it rules out R4C7 and R10C7. Cross those squares out.
  14. Row 4 has only one open square left: R4C8. Put a cat there.
  15. The Blue region has only one open square left: R10C9. Put a cat there.
  16. The Green region has only one open square left: R8C6. Put a cat there.
  17. The Red region has only one open square left: R1C5. Put a cat there.
  18. The Brown region has only one open square left: R6C7. Put a cat there.

About this puzzle

Where to start: the Yellow region is a single square, so its cat is already decided. Its 10 color regions range from 1 square (Yellow) to 20 squares. It can be solved in 18 deduction steps using grouped row/column/region deductions.

If a row and a color both have only two open squares and share them, those two lines are locked together -- neither can use squares anywhere else.

Every puzzle on this site has exactly one solution that can be reached by pure deduction. If you find yourself guessing, look again for a region or line with only a few open squares left.

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