Find the Cat #285: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (13)Orange (4)Yellow (12)Green (1)Teal (6)Blue (12)Purple (10)Pink (26)Brown (9)Grey (7)

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 Green region has only one open square left: R2C3. Put a cat there.
  2. Wherever the cat in the Orange region ends up, it rules out R4C9 and R5C7. Cross those squares out.
  3. Wherever the cat in the Purple region ends up, it rules out R10C4. Cross that square out.
  4. The Teal and Brown regions can only use rows 1 and 3, so rows 1 and 3 are already spoken for. Cross out R1C1, R1C5, R3C1, R3C5 and R3C10.
  5. Wherever the cat in the Blue region ends up, it rules out R5C4. Cross that square out.
  6. The Red and Grey regions can only use columns 1 and 2, so columns 1 and 2 are already spoken for. Cross out R10C2.
  7. Wherever the cat in the Purple region ends up, it rules out R4C4, R6C5, R7C5, R8C4 and R9C4. Cross those squares out.
  8. Wherever the cat in the Blue region ends up, it rules out R4C6. Cross that square out.
  9. Wherever the cat in the Orange region ends up, it rules out R3C8. Cross that square out.
  10. The Orange and Blue regions can only use rows 4 and 5, so rows 4 and 5 are already spoken for. Cross out R4C1, R4C2, R4C10, R5C1, R5C2, R5C9 and 1 more.
  11. Wherever the cat in the Red region ends up, it rules out R6C2, R7C2, R8C1, R9C1 and R10C1. Cross those squares out.
  12. The Red and Purple regions can only use rows 6 and 7, so rows 6 and 7 are already spoken for. Cross out R6C6, R6C7, R6C8, R6C9, R6C10, R7C6 and 4 more.
  13. The Yellow and Blue regions can only use columns 5 and 6, so columns 5 and 6 are already spoken for. Cross out R1C6, R3C6, R8C6 and R10C6.
  14. The Teal region has only one open square left: R1C7. Put a cat there.
  15. The Brown region has only one open square left: R3C9. Put a cat there.
  16. The Orange region has only one open square left: R5C8. Put a cat there.
  17. The Blue region has only one open square left: R4C5. Put a cat there.
  18. The Yellow region has only one open square left: R9C6. Put a cat there.
  19. The Grey region has only one open square left: R8C2. Put a cat there.
  20. The Red region has only one open square left: R6C1. Put a cat there.
  21. The Purple region has only one open square left: R7C4. Put a cat there.
  22. The Pink region has only one open square left: R10C10. Put a cat there.

About this puzzle

Where to start: the Green region is a single square, so its cat is already decided. Its 10 color regions range from 1 square (Green) to 26 squares. It can be solved in 22 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