Find the Cat #263: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (1)Orange (10)Yellow (16)Green (7)Teal (7)Blue (19)Purple (11)Pink (7)Brown (11)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 Red region has only one open square left: R4C1. Put a cat there.
  2. Wherever the cat in the Teal region ends up, it rules out R2C9. Cross that square out.
  3. Wherever the cat in the Brown region ends up, it rules out R1C3, R2C3, R7C3, R8C3, R9C3 and R10C3. Cross those squares out.
  4. Wherever the cat in the Pink region ends up, it rules out R1C2, R2C2, R6C2, R7C2 and R8C2. Cross those squares out.
  5. Wherever the cat in the Grey region ends up, it rules out R1C4, R2C4, R3C4, R6C3, R6C5, R8C4 and 2 more. Cross those squares out.
  6. Wherever the cat in the Green region ends up, it rules out R8C6. Cross that square out.
  7. The Orange, Yellow, Teal and Brown regions can only use rows 1, 2, 3 and 5, so rows 1, 2, 3 and 5 are already spoken for. Cross out R5C4, R5C6, R5C7, R5C8, R5C9 and R5C10.
  8. Wherever the cat in the Grey region ends up, it rules out R7C5. Cross that square out.
  9. Wherever the cat in the Green region ends up, it rules out R9C6. Cross that square out.
  10. Wherever the cat in row 5 ends up, it rules out R6C4. Cross that square out.
  11. The Grey region has only one open square left: R7C4. Put a cat there.
  12. The Green region has only one open square left: R9C5. Put a cat there.
  13. The Pink region has only one open square left: R10C2. Put a cat there.
  14. Row 5 has only one open square left: R5C3. Put a cat there.
  15. Wherever the cat in the Orange region ends up, it rules out R2C6, R2C7, R3C8, R3C9 and R3C10. Cross those squares out.
  16. Wherever the cat in the Yellow region ends up, it rules out R1C8 and R1C9. Cross those squares out.
  17. Wherever the cat in the Teal region ends up, it rules out R6C10 and R8C10. Cross those squares out.
  18. Wherever the cat in the Purple region ends up, it rules out R6C8 and R6C9. Cross those squares out.
  19. Column 9 has only one open square left: R8C9. Put a cat there.
  20. Column 8 has only one open square left: R2C8. Put a cat there.
  21. The Orange region has only one open square left: R3C6. Put a cat there.
  22. The Teal region has only one open square left: R1C10. Put a cat there.
  23. The Purple region has only one open square left: R6C7. 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 19 squares. It can be solved in 23 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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