Find the Cat #216: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (1)Orange (16)Yellow (11)Green (6)Teal (9)Blue (8)Purple (7)Pink (13)Brown (20)Grey (9)

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: R5C3. Put a cat there.
  2. Wherever the cat in the Green region ends up, it rules out R2C1 and R3C1. Cross those squares out.
  3. Wherever the cat in the Teal region ends up, it rules out R7C1 and R7C2. Cross those squares out.
  4. Wherever the cat in the Purple region ends up, it rules out R9C2. Cross that square out.
  5. Wherever the cat in row 1 ends up, it rules out R2C2, R2C4, R2C6, R2C7, R2C8, R3C6 and 2 more. Cross those squares out.
  6. The Green and Purple regions can only use columns 1 and 2, so columns 1 and 2 are already spoken for. Cross out R1C1, R1C2, R6C1 and R8C2.
  7. The Teal region has only one open square left: R7C4. Put a cat there.
  8. The Blue region has only one open square left: R9C5. Put a cat there.
  9. The Yellow region has only one open square left: R10C7. Put a cat there.
  10. The Purple region has only one open square left: R8C1. Put a cat there.
  11. The Green region has only one open square left: R3C2. Put a cat there.
  12. Wherever the cat in the Orange region ends up, it rules out R6C6. Cross that square out.
  13. The Pink region has only one open square left: R4C6. Put a cat there.
  14. Wherever the cat in the Brown region ends up, it rules out R2C9. Cross that square out.
  15. The Grey region has only one open square left: R2C10. Put a cat there.
  16. The Brown region has only one open square left: R1C8. Put a cat there.
  17. The Orange region has only one open square left: R6C9. 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 20 squares. It can be solved in 17 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