Find the Cat #233: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (1)Orange (20)Yellow (12)Green (16)Teal (8)Blue (10)Purple (5)Pink (10)Brown (10)Grey (8)

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: R2C1. Put a cat there.
  2. Wherever the cat in the Teal region ends up, it rules out R4C2, R5C2, R6C2, R8C2 and R9C2. Cross those squares out.
  3. Wherever the cat in the Blue region ends up, it rules out R3C4 and R5C3. Cross those squares out.
  4. Wherever the cat in the Purple region ends up, it rules out R6C3, R7C2 and R8C4. Cross those squares out.
  5. The Teal region has only one open square left: R10C2. Put a cat there.
  6. Wherever the cat in the Yellow region ends up, it rules out R8C5, R9C7, R9C8, R9C9 and R9C10. Cross those squares out.
  7. Wherever the cat in the Grey region ends up, it rules out R6C6. Cross that square out.
  8. Wherever the cat in row 1 ends up, it rules out R3C7, R3C8, R3C9, R4C7, R4C8 and R4C9. Cross those squares out.
  9. The Blue and Purple regions can only use columns 3 and 4, so columns 3 and 4 are already spoken for. Cross out R1C3, R1C4, R6C4 and R9C4.
  10. Wherever the cat in the Yellow region ends up, it rules out R8C6. Cross that square out.
  11. Wherever the cat in the Grey region ends up, it rules out R1C5, R3C5, R4C5 and R9C5. Cross those squares out.
  12. The Yellow region has only one open square left: R9C6. Put a cat there.
  13. The Pink region has only one open square left: R5C7. Put a cat there.
  14. Wherever the cat in the Green region ends up, it rules out R7C9. Cross that square out.
  15. Wherever the cat in the Grey region ends up, it rules out R7C4. Cross that square out.
  16. Column 4 has only one open square left: R4C4. Put a cat there.
  17. Row 3 has only one open square left: R3C10. Put a cat there.
  18. The Green region has only one open square left: R7C8. Put a cat there.
  19. The Orange region has only one open square left: R1C9. Put a cat there.
  20. The Purple region has only one open square left: R8C3. Put a cat there.
  21. The Grey region has only one open square left: R6C5. 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 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.

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