Find the Cat #207: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (5)Orange (8)Yellow (5)Green (23)Teal (3)Blue (15)Purple (21)Pink (9)Brown (1)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 Brown region has only one open square left: R1C5. Put a cat there.
  2. The Yellow region has only one open square left: R2C10. Put a cat there.
  3. The Orange region has only one open square left: R3C6. Put a cat there.
  4. Wherever the cat in the Red region ends up, it rules out R6C2 and R8C1. Cross those squares out.
  5. Wherever the cat in the Teal region ends up, it rules out R4C1, R5C1, R6C1, R7C1, R9C2 and R10C2. Cross those squares out.
  6. Wherever the cat in the Red region ends up, it rules out R4C2, R5C2, R7C3 and R8C3. Cross those squares out.
  7. Wherever the cat in the Grey region ends up, it rules out R4C3. Cross that square out.
  8. Wherever the cat in the Purple region ends up, it rules out R8C4, R9C4 and R10C4. Cross those squares out.
  9. Wherever the cat in the Blue region ends up, it rules out R7C7 and R9C8. Cross those squares out.
  10. The Red, Teal, Blue and Pink regions can only use rows 7, 8, 9 and 10, so rows 7, 8, 9 and 10 are already spoken for. Cross out R7C4, R7C8, R9C3 and R10C3.
  11. Wherever the cat in the Purple region ends up, it rules out R5C3. Cross that square out.
  12. The Grey region has only one open square left: R6C3. Put a cat there.
  13. The Red region has only one open square left: R8C2. Put a cat there.
  14. The Teal region has only one open square left: R10C1. Put a cat there.
  15. The Blue region has only one open square left: R9C7. Put a cat there.
  16. The Purple region has only one open square left: R4C4. Put a cat there.
  17. The Pink region has only one open square left: R7C9. Put a cat there.
  18. The Green region has only one open square left: R5C8. Put a cat there.

About this puzzle

Where to start: the Brown region is a single square, so its cat is already decided. Its 10 color regions range from 1 square (Brown) to 23 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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