Find the Cat #227: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (9)Orange (19)Yellow (8)Green (6)Teal (21)Blue (2)Purple (13)Pink (10)Brown (1)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 Brown region has only one open square left: R4C10. Put a cat there.
  2. Wherever the cat in the Green region ends up, it rules out R1C8, R1C9, R2C1, R2C2, R2C3, R2C4 and 4 more. Cross those squares out.
  3. Wherever the cat in the Blue region ends up, it rules out R9C2, R9C3, R10C1, R10C4, R10C5, R10C6 and 3 more. Cross those squares out.
  4. Wherever the cat in the Grey region ends up, it rules out R8C8. Cross that square out.
  5. The Pink and Grey regions can only use rows 8 and 9, so rows 8 and 9 are already spoken for. Cross out R8C1, R8C2, R8C4, R8C5, R8C6, R8C7 and 2 more.
  6. The Green and Grey regions can only use columns 8 and 9, so columns 8 and 9 are already spoken for. Cross out R5C8, R6C8, R6C9, R7C8 and R7C9.
  7. The Red region has only one open square left: R6C7. Put a cat there.
  8. The Teal region has only one open square left: R5C5. Put a cat there.
  9. Wherever the cat in the Yellow region ends up, it rules out R3C3, R3C4 and R3C6. Cross those squares out.
  10. Column 6 has only one open square left: R1C6. Put a cat there.
  11. Wherever the cat in the Pink region ends up, it rules out R7C4 and R10C3. Cross those squares out.
  12. The Blue region has only one open square left: R10C2. Put a cat there.
  13. The Yellow region has only one open square left: R3C1. Put a cat there.
  14. The Orange region has only one open square left: R7C3. Put a cat there.
  15. The Pink region has only one open square left: R9C4. Put a cat there.
  16. The Grey region has only one open square left: R8C9. Put a cat there.
  17. The Green region has only one open square left: R2C8. 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 21 squares. It can be solved in 17 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.

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