Find the Cat #217: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (11)Orange (11)Yellow (6)Green (14)Teal (1)Blue (18)Purple (15)Pink (4)Brown (15)Grey (5)

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 Teal region has only one open square left: R9C3. Put a cat there.
  2. Wherever the cat in the Red region ends up, it rules out R1C1, R2C1, R3C1, R4C1, R5C1, R6C1 and 1 more. Cross those squares out.
  3. Wherever the cat in the Pink region ends up, it rules out R1C10, R6C10, R7C10, R8C10 and R10C10. Cross those squares out.
  4. Wherever the cat in the Yellow region ends up, it rules out R1C9, R2C9, R3C9, R4C9, R5C9, R6C9 and 1 more. Cross those squares out.
  5. Wherever the cat in the Grey region ends up, it rules out R5C8, R6C6 and R7C7. Cross those squares out.
  6. The Red and Yellow regions can only use rows 8 and 10, so rows 8 and 10 are already spoken for. Cross out R8C5, R8C6, R8C7, R8C8, R10C5, R10C6 and 2 more.
  7. The Brown region has only one open square left: R7C8. Put a cat there.
  8. The Yellow region has only one open square left: R10C9. Put a cat there.
  9. The Red region has only one open square left: R8C1. Put a cat there.
  10. The Grey region has only one open square left: R5C7. Put a cat there.
  11. The Orange region has only one open square left: R6C5. Put a cat there.
  12. Wherever the cat in the Green region ends up, it rules out R3C4 and R4C2. Cross those squares out.
  13. The Blue region has only one open square left: R3C6. Put a cat there.
  14. The Green region has only one open square left: R4C4. Put a cat there.
  15. The Pink region has only one open square left: R2C10. Put a cat there.
  16. The Purple region has only one open square left: R1C2. Put a cat there.

About this puzzle

Where to start: the Teal region is a single square, so its cat is already decided. Its 10 color regions range from 1 square (Teal) to 18 squares. It can be solved in 16 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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