Find the Cat #257: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (15)Orange (20)Yellow (16)Green (11)Teal (14)Blue (6)Purple (10)Pink (2)Brown (1)Grey (5)

A 10x10 logic grid, 10 colors, 10 cats. Work out where each cat sits using nothing but the rules -- there is only one correct layout and no guessing is needed.

  • 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: R1C2. Put a cat there.
  2. Wherever the cat in the Blue region ends up, it rules out R4C3 and R6C4. Cross those squares out.
  3. Wherever the cat in the Teal region ends up, it rules out R3C5, R3C6 and R3C7. Cross those squares out.
  4. Wherever the cat in the Pink region ends up, it rules out R2C9, R3C9, R4C8, R4C10, R5C8, R5C10 and 5 more. Cross those squares out.
  5. The Green, Blue and Grey regions can only use columns 1, 3 and 4, so columns 1, 3 and 4 are already spoken for. Cross out R2C4, R3C1, R3C3, R3C4, R4C4, R7C4 and 2 more.
  6. The Teal region has only one open square left: R2C6. Put a cat there.
  7. Wherever the cat in the Purple region ends up, it rules out R5C4, R6C5, R7C5, R8C5, R9C5 and R10C5. Cross those squares out.
  8. Column 4 has only one open square left: R10C4. Put a cat there.
  9. Wherever the cat in the Yellow region ends up, it rules out R7C7, R7C8, R8C1, R8C3, R8C10, R9C7 and 1 more. Cross those squares out.
  10. Row 9 has only one open square left: R9C10. Put a cat there.
  11. Row 3 has only one open square left: R3C8. Put a cat there.
  12. The Yellow region has only one open square left: R8C7. Put a cat there.
  13. The Pink region has only one open square left: R5C9. Put a cat there.
  14. The Blue region has only one open square left: R6C3. Put a cat there.
  15. The Purple region has only one open square left: R4C5. Put a cat there.
  16. The Green region has only one open square left: R7C1. 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 20 squares. It can be solved in 16 deduction steps using grouped row/column/region deductions.

Start with the region that is a single square -- its cat has nowhere else to go. Cross out that cat's whole row, column and neighbors, then move on to the next-smallest regions: with only a couple of squares each, they leave very little room.

Stuck? Open the step-by-step solution below -- each step names the row, column or color involved, so you can use it as a hint and then finish the puzzle yourself.

More hard puzzles