Find the Cat #255: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (1)Orange (12)Yellow (12)Green (7)Teal (27)Blue (9)Purple (8)Pink (11)Brown (8)Grey (5)

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: R3C10. Put a cat there.
  2. Wherever the cat in the Orange region ends up, it rules out R1C7. Cross that square out.
  3. Wherever the cat in the Purple region ends up, it rules out R1C1 and R1C2. Cross those squares out.
  4. Wherever the cat in the Brown region ends up, it rules out R7C1, R8C1, R9C1 and R10C1. Cross those squares out.
  5. Wherever the cat in the Grey region ends up, it rules out R2C2, R4C2, R5C2, R6C2, R7C2, R8C3 and 2 more. Cross those squares out.
  6. Wherever the cat in the Blue region ends up, it rules out R1C4. Cross that square out.
  7. Wherever the cat in the Pink region ends up, it rules out R1C3, R2C3 and R10C3. Cross those squares out.
  8. The Orange, Green, Blue and Brown regions can only use rows 2, 4, 5 and 6, so rows 2, 4, 5 and 6 are already spoken for. Cross out R4C3, R4C8, R5C3, R5C8, R5C9, R6C3 and 4 more.
  9. The Pink region has only one open square left: R7C3. Put a cat there.
  10. The Grey region has only one open square left: R9C2. Put a cat there.
  11. Wherever the cat in the Yellow region ends up, it rules out R10C5. Cross that square out.
  12. The Yellow and Blue regions can only use columns 4 and 5, so columns 4 and 5 are already spoken for. Cross out R1C5, R4C5, R5C4, R5C5 and R6C5.
  13. Row 6 has only one open square left: R6C1. Put a cat there.
  14. Wherever the cat in the Green region ends up, it rules out R1C6, R2C6, R4C7, R5C7, R8C6 and R10C6. Cross those squares out.
  15. Row 5 has only one open square left: R5C6. Put a cat there.
  16. Row 4 has only one open square left: R4C4. Put a cat there.
  17. The Yellow region has only one open square left: R8C5. Put a cat there.
  18. Wherever the cat in the Orange region ends up, it rules out R1C8. Cross that square out.
  19. The Purple region has only one open square left: R1C9. Put a cat there.
  20. The Orange region has only one open square left: R2C7. Put a cat there.
  21. The Teal region has only one open square left: R10C8. 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 27 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.

When you fill the last cat, press Check Answer -- the grid is verified against the stored solution and any broken rule is named so you know where to look.

More hard puzzles