Find the Cat #251: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (22)Orange (10)Yellow (9)Green (11)Teal (6)Blue (7)Purple (9)Pink (9)Brown (1)Grey (16)

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 Brown region has only one open square left: R4C2. Put a cat there.
  2. Wherever the cat in the Blue region ends up, it rules out R6C5. Cross that square out.
  3. The Teal, Purple and Pink regions can only use rows 1, 2 and 3, so rows 1, 2 and 3 are already spoken for. Cross out R1C9, R1C10, R2C7, R2C8, R2C9, R2C10 and 4 more.
  4. Wherever the cat in row 3 ends up, it rules out R2C5. Cross that square out.
  5. Wherever the cat in column 10 ends up, it rules out R9C9. Cross that square out.
  6. The Orange and Pink regions can only use columns 1 and 3, so columns 1 and 3 are already spoken for. Cross out R2C3, R6C3, R7C3, R9C3 and R10C3.
  7. The Green and Purple regions can only use columns 4 and 5, so columns 4 and 5 are already spoken for. Cross out R1C5, R5C4, R5C5, R9C4, R9C5, R10C4 and 1 more.
  8. Wherever the cat in the Blue region ends up, it rules out R1C6, R2C6, R3C6, R6C7, R8C6, R9C6 and 1 more. Cross those squares out.
  9. Wherever the cat in the Teal region ends up, it rules out R1C1, R1C3 and R1C4. Cross those squares out.
  10. The Pink region has only one open square left: R2C1. Put a cat there.
  11. The Orange region has only one open square left: R8C3. Put a cat there.
  12. Wherever the cat in the Green region ends up, it rules out R6C6. Cross that square out.
  13. Wherever the cat in row 9 ends up, it rules out R10C7, R10C8 and R10C9. Cross those squares out.
  14. Row 10 has only one open square left: R10C10. Put a cat there.
  15. Row 9 has only one open square left: R9C8. Put a cat there.
  16. The Teal region has only one open square left: R1C7. Put a cat there.
  17. The Red region has only one open square left: R6C9. Put a cat there.
  18. The Green region has only one open square left: R7C5. Put a cat there.
  19. The Blue region has only one open square left: R5C6. Put a cat there.
  20. The Purple region has only one open square left: R3C4. Put a cat there.

About this puzzle

Where to start: the Brown region is a single square, so its cat is already decided. Its 10 color regions range from 1 square (Brown) to 22 squares. It can be solved in 20 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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