Find the Cat #211: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (16)Orange (9)Yellow (1)Green (15)Teal (6)Blue (4)Purple (10)Pink (9)Brown (20)Grey (10)

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: R8C8. Put a cat there.
  2. Wherever the cat in the Orange region ends up, it rules out R5C6. Cross that square out.
  3. Wherever the cat in the Blue region ends up, it rules out R1C1, R1C2, R1C3, R1C4, R1C9, R1C10 and 1 more. Cross those squares out.
  4. Wherever the cat in the Teal region ends up, it rules out R3C9. Cross that square out.
  5. Wherever the cat in row 9 ends up, it rules out R10C2. Cross that square out.
  6. Wherever the cat in row 10 ends up, it rules out R9C2. Cross that square out.
  7. The Teal, Purple, Pink and Grey regions can only use rows 2, 3, 4 and 5, so rows 2, 3, 4 and 5 are already spoken for. Cross out R3C2, R4C2, R4C9, R4C10, R5C2, R5C3 and 3 more.
  8. The Orange and Green regions can only use rows 6 and 7, so rows 6 and 7 are already spoken for. Cross out R6C1, R6C2, R6C3, R6C4, R7C1, R7C2 and 3 more.
  9. Column 2 has only one open square left: R2C2. Put a cat there.
  10. The Teal region has only one open square left: R3C10. Put a cat there.
  11. The Green region has only one open square left: R6C9. Put a cat there.
  12. The Orange region has only one open square left: R7C6. Put a cat there.
  13. The Pink region has only one open square left: R4C7. Put a cat there.
  14. The Blue region has only one open square left: R1C5. Put a cat there.
  15. The Purple region has only one open square left: R5C4. Put a cat there.
  16. The Red region has only one open square left: R10C3. Put a cat there.
  17. The Brown region has only one open square left: R9C1. 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 17 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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