Find the Cat #273: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (16)Orange (8)Yellow (10)Green (12)Teal (16)Blue (7)Purple (8)Pink (7)Brown (1)Grey (15)

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: R1C1. Put a cat there.
  2. Wherever the cat in the Purple region ends up, it rules out R3C4 and R4C3. Cross those squares out.
  3. Wherever the cat in the Pink region ends up, it rules out R7C2, R8C4 and R9C3. Cross those squares out.
  4. The Purple and Pink regions can only use columns 2 and 3, so columns 2 and 3 are already spoken for. Cross out R4C2, R5C2, R5C3, R6C2, R6C3, R9C2 and 2 more.
  5. Wherever the cat in the Yellow region ends up, it rules out R9C6. Cross that square out.
  6. Wherever the cat in the Teal region ends up, it rules out R6C5 and R7C3. Cross those squares out.
  7. Wherever the cat in the Pink region ends up, it rules out R8C5, R8C6, R8C7, R8C8, R8C9 and R8C10. Cross those squares out.
  8. Wherever the cat in the Orange region ends up, it rules out R10C8. Cross that square out.
  9. Wherever the cat in the Yellow region ends up, it rules out R9C7, R9C8, R9C9, R9C10, R10C4 and R10C5. Cross those squares out.
  10. Wherever the cat in the Orange region ends up, it rules out R10C9 and R10C10. Cross those squares out.
  11. Wherever the cat in row 5 ends up, it rules out R4C9, R6C9 and R7C10. Cross those squares out.
  12. Wherever the cat in column 9 ends up, it rules out R6C10. Cross that square out.
  13. Wherever the cat in column 10 ends up, it rules out R2C9 and R3C9. Cross those squares out.
  14. Wherever the cat in column 9 ends up, it rules out R4C4, R4C5, R4C8, R5C4, R5C5, R5C6 and 4 more. Cross those squares out.
  15. Wherever the cat in the Green region ends up, it rules out R7C6. Cross that square out.
  16. Wherever the cat in row 4 ends up, it rules out R2C10. Cross that square out.
  17. Wherever the cat in row 5 ends up, it rules out R4C10. Cross that square out.
  18. Wherever the cat in row 4 ends up, it rules out R2C4, R2C5, R2C6, R2C7, R2C8, R3C5 and 2 more. Cross those squares out.
  19. Row 2 has only one open square left: R2C3. Put a cat there.
  20. The Pink region has only one open square left: R8C2. Put a cat there.
  21. Wherever the cat in row 3 ends up, it rules out R5C10. Cross that square out.
  22. Row 5 has only one open square left: R5C9. Put a cat there.
  23. Column 10 has only one open square left: R3C10. Put a cat there.
  24. Column 8 has only one open square left: R7C8. Put a cat there.
  25. The Teal region has only one open square left: R6C4. Put a cat there.
  26. The Yellow region has only one open square left: R9C5. Put a cat there.
  27. The Orange region has only one open square left: R10C7. Put a cat there.
  28. The Red region has only one open square left: R4C6. 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 16 squares. It can be solved in 28 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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