Find the Cat #224: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (6)Orange (11)Yellow (13)Green (14)Teal (4)Blue (8)Purple (15)Pink (17)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: R1C10. Put a cat there.
  2. The Blue region has only one open square left: R2C7. Put a cat there.
  3. The Yellow region has only one open square left: R3C9. Put a cat there.
  4. Wherever the cat in the Green region ends up, it rules out R4C1, R4C2, R4C5, R4C6, R5C3 and R5C4. Cross those squares out.
  5. Wherever the cat in the Red region ends up, it rules out R5C1, R5C2, R5C8, R6C5 and R6C6. Cross those squares out.
  6. The Brown region has only one open square left: R6C8. Put a cat there.
  7. Wherever the cat in the Teal region ends up, it rules out R8C1 and R10C2. Cross those squares out.
  8. Wherever the cat in column 1 ends up, it rules out R8C2. Cross that square out.
  9. Wherever the cat in column 2 ends up, it rules out R8C3, R9C3 and R10C3. Cross those squares out.
  10. Wherever the cat in the Pink region ends up, it rules out R7C4. Cross that square out.
  11. Wherever the cat in row 8 ends up, it rules out R7C5, R9C5 and R9C6. Cross those squares out.
  12. Wherever the cat in the Purple region ends up, it rules out R10C4. Cross that square out.
  13. Wherever the cat in the Pink region ends up, it rules out R7C6. Cross that square out.
  14. Wherever the cat in the Orange region ends up, it rules out R8C4. Cross that square out.
  15. The Red and Orange regions can only use columns 5 and 6, so columns 5 and 6 are already spoken for. Cross out R10C5 and R10C6.
  16. The Purple region has only one open square left: R9C4. Put a cat there.
  17. The Orange region has only one open square left: R8C6. Put a cat there.
  18. The Red region has only one open square left: R5C5. Put a cat there.
  19. The Green region has only one open square left: R4C3. Put a cat there.
  20. The Teal region has only one open square left: R10C1. Put a cat there.
  21. The Pink region has only one open square left: R7C2. 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 17 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.

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