Find the Cat #238: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (1)Orange (15)Yellow (17)Green (8)Teal (18)Blue (7)Purple (3)Pink (9)Brown (10)Grey (12)

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 Red region has only one open square left: R7C6. Put a cat there.
  2. The Purple region has only one open square left: R1C5. Put a cat there.
  3. The Green region has only one open square left: R4C4. Put a cat there.
  4. Wherever the cat in the Blue region ends up, it rules out R2C1, R2C2, R2C3, R2C7 and R3C9. Cross those squares out.
  5. Wherever the cat in the Orange region ends up, it rules out R6C1. Cross that square out.
  6. Wherever the cat in the Grey region ends up, it rules out R5C2. Cross that square out.
  7. Wherever the cat in the Orange region ends up, it rules out R8C1, R9C1 and R10C1. Cross those squares out.
  8. Wherever the cat in the Pink region ends up, it rules out R9C3. Cross that square out.
  9. Wherever the cat in row 9 ends up, it rules out R10C3. Cross that square out.
  10. The Orange, Brown and Grey regions can only use rows 3, 5 and 6, so rows 3, 5 and 6 are already spoken for. Cross out R3C7, R5C7, R5C9, R6C8 and R6C9.
  11. The Yellow region has only one open square left: R8C8. Put a cat there.
  12. Column 3 has only one open square left: R6C3. Put a cat there.
  13. Column 7 has only one open square left: R10C7. Put a cat there.
  14. The Pink region has only one open square left: R9C2. Put a cat there.
  15. Column 9 has only one open square left: R2C9. Put a cat there.
  16. The Brown region has only one open square left: R5C10. Put a cat there.
  17. The Orange region has only one open square left: R3C1. Put a cat there.

About this puzzle

Where to start: the Red region is a single square, so its cat is already decided. Its 10 color regions range from 1 square (Red) to 18 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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