Find the Cat #262: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (10)Orange (12)Yellow (7)Green (1)Teal (13)Blue (11)Purple (15)Pink (10)Brown (7)Grey (14)

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 Green region has only one open square left: R2C10. Put a cat there.
  2. The Yellow region has only one open square left: R4C9. Put a cat there.
  3. Wherever the cat in the Teal region ends up, it rules out R1C7. Cross that square out.
  4. Wherever the cat in the Blue region ends up, it rules out R7C7, R7C8, R8C1, R8C2, R8C3, R8C4 and 4 more. Cross those squares out.
  5. Wherever the cat in the Brown region ends up, it rules out R1C1, R1C2, R1C3, R1C4 and R1C8. Cross those squares out.
  6. Wherever the cat in the Teal region ends up, it rules out R6C7, R8C7 and R10C7. Cross those squares out.
  7. The Blue region has only one open square left: R8C8. Put a cat there.
  8. The Orange and Teal regions can only use rows 3 and 5, so rows 3 and 5 are already spoken for. Cross out R3C1, R3C2, R5C1, R5C2, R5C3, R5C5 and 1 more.
  9. The Red region has only one open square left: R6C1. Put a cat there.
  10. The Pink region has only one open square left: R7C6. Put a cat there.
  11. The Brown region has only one open square left: R1C5. Put a cat there.
  12. Wherever the cat in the Purple region ends up, it rules out R9C2, R10C3 and R10C4. Cross those squares out.
  13. The Grey region has only one open square left: R10C2. Put a cat there.
  14. The Purple region has only one open square left: R9C4. Put a cat there.
  15. The Orange region has only one open square left: R3C3. Put a cat there.
  16. The Teal region has only one open square left: R5C7. Put a cat there.

About this puzzle

Where to start: the Green region is a single square, so its cat is already decided. Its 10 color regions range from 1 square (Green) to 15 squares. It can be solved in 16 deduction steps using grouped row/column/region deductions.

A useful habit is to mark squares you have ruled out. Tap a square once for a cross and twice for a cat -- crosses cost nothing and make later deductions much easier to spot.

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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