Find the Cat #287: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (16)Orange (4)Yellow (10)Green (8)Teal (15)Blue (8)Purple (1)Pink (18)Brown (11)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 Purple region has only one open square left: R3C4. Put a cat there.
  2. Wherever the cat in the Orange region ends up, it rules out R9C5 and R10C7. Cross those squares out.
  3. Wherever the cat in the Blue region ends up, it rules out R6C6. Cross that square out.
  4. The Orange, Green and Grey regions can only use rows 8, 9 and 10, so rows 8, 9 and 10 are already spoken for. Cross out R8C1, R8C2, R8C3, R8C6, R8C8, R8C9 and 3 more.
  5. Wherever the cat in the Brown region ends up, it rules out R6C2. Cross that square out.
  6. Wherever the cat in row 8 ends up, it rules out R7C6 and R9C6. Cross those squares out.
  7. Wherever the cat in the Orange region ends up, it rules out R10C1, R10C2, R10C3, R10C8, R10C9 and R10C10. Cross those squares out.
  8. Wherever the cat in column 1 ends up, it rules out R1C2, R1C3, R2C2, R4C2 and R5C2. Cross those squares out.
  9. Column 2 has only one open square left: R7C2. Put a cat there.
  10. The Blue region has only one open square left: R6C5. Put a cat there.
  11. The Orange region has only one open square left: R10C6. Put a cat there.
  12. The Green region has only one open square left: R9C3. Put a cat there.
  13. The Grey region has only one open square left: R8C7. Put a cat there.
  14. The Red region has only one open square left: R5C8. Put a cat there.
  15. Wherever the cat in the Yellow region ends up, it rules out R1C1, R2C9 and R2C10. Cross those squares out.
  16. The Teal region has only one open square left: R4C10. Put a cat there.
  17. The Yellow region has only one open square left: R1C9. Put a cat there.
  18. The Pink region has only one open square left: R2C1. Put a cat there.

About this puzzle

Where to start: the Purple region is a single square, so its cat is already decided. Its 10 color regions range from 1 square (Purple) to 18 squares. It can be solved in 18 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.

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