Find the Cat #293: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (8)Orange (11)Yellow (13)Green (11)Teal (6)Blue (11)Purple (16)Pink (1)Brown (12)Grey (11)

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 Pink region has only one open square left: R1C7. Put a cat there.
  2. Wherever the cat in the Red region ends up, it rules out R7C5. Cross that square out.
  3. Wherever the cat in the Grey region ends up, it rules out R3C4, R3C5 and R4C5. Cross those squares out.
  4. Wherever the cat in the Teal region ends up, it rules out R2C2. Cross that square out.
  5. The Teal and Grey regions can only use rows 2 and 3, so rows 2 and 3 are already spoken for. Cross out R2C1, R2C9, R2C10, R3C1, R3C2, R3C8 and 2 more.
  6. Wherever the cat in column 10 ends up, it rules out R9C9. Cross that square out.
  7. Wherever the cat in row 9 ends up, it rules out R10C2. Cross that square out.
  8. Wherever the cat in column 2 ends up, it rules out R5C1. Cross that square out.
  9. The Green and Blue regions can only use rows 4 and 5, so rows 4 and 5 are already spoken for. Cross out R4C9, R4C10, R5C2, R5C4, R5C5, R5C8 and 2 more.
  10. Wherever the cat in the Yellow region ends up, it rules out R7C9. Cross that square out.
  11. The Red, Orange and Yellow regions can only use rows 6, 7 and 8, so rows 6, 7 and 8 are already spoken for. Cross out R6C1, R7C1, R7C2, R8C1, R8C2, R8C3 and 2 more.
  12. The Red and Blue regions can only use columns 6 and 8, so columns 6 and 8 are already spoken for. Cross out R3C6, R6C8, R9C6, R9C8, R10C6 and R10C8.
  13. The Grey region has only one open square left: R2C5. Put a cat there.
  14. The Teal region has only one open square left: R3C3. Put a cat there.
  15. The Green region has only one open square left: R4C1. Put a cat there.
  16. The Blue region has only one open square left: R5C6. Put a cat there.
  17. The Red region has only one open square left: R7C8. Put a cat there.
  18. The Brown region has only one open square left: R9C2. Put a cat there.
  19. The Orange region has only one open square left: R6C4. Put a cat there.
  20. The Yellow region has only one open square left: R8C10. Put a cat there.
  21. The Purple region has only one open square left: R10C9. Put a cat there.

About this puzzle

Where to start: the Pink region is a single square, so its cat is already decided. Its 10 color regions range from 1 square (Pink) to 16 squares. It can be solved in 21 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