Find the Cat #264: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (9)Orange (20)Yellow (6)Green (14)Teal (10)Blue (9)Purple (7)Pink (13)Brown (11)Grey (1)

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 Grey region has only one open square left: R6C8. Put a cat there.
  2. The Purple region has only one open square left: R4C7. Put a cat there.
  3. Wherever the cat in the Red region ends up, it rules out R2C10 and R3C10. Cross those squares out.
  4. Wherever the cat in the Yellow region ends up, it rules out R1C1, R1C2, R1C3, R1C4, R1C5, R1C6 and 1 more. Cross those squares out.
  5. Wherever the cat in the Blue region ends up, it rules out R5C3. Cross that square out.
  6. Wherever the cat in the Teal region ends up, it rules out R2C2. Cross that square out.
  7. The Orange and Teal regions can only use rows 2 and 3, so rows 2 and 3 are already spoken for. Cross out R3C9.
  8. The Red region has only one open square left: R5C10. Put a cat there.
  9. The Yellow region has only one open square left: R1C9. Put a cat there.
  10. The Blue region has only one open square left: R7C3. Put a cat there.
  11. The Pink region has only one open square left: R9C6. Put a cat there.
  12. Row 8 has only one open square left: R8C1. Put a cat there.
  13. The Teal region has only one open square left: R3C2. Put a cat there.
  14. The Green region has only one open square left: R10C4. Put a cat there.
  15. The Orange region has only one open square left: R2C5. Put a cat there.

About this puzzle

Where to start: the Grey region is a single square, so its cat is already decided. Its 10 color regions range from 1 square (Grey) to 20 squares. It can be solved in 15 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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