Find the Cat #294: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (9)Orange (13)Yellow (12)Green (14)Teal (14)Blue (6)Purple (4)Pink (8)Brown (1)Grey (19)

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: R9C1. Put a cat there.
  2. The Purple region has only one open square left: R10C10. Put a cat there.
  3. Wherever the cat in the Red region ends up, it rules out R3C3. Cross that square out.
  4. Wherever the cat in the Orange region ends up, it rules out R7C5, R7C6, R8C3, R8C4, R8C7, R8C8 and 1 more. Cross those squares out.
  5. Wherever the cat in the Yellow region ends up, it rules out R6C8. Cross that square out.
  6. Wherever the cat in the Green region ends up, it rules out R5C4 and R6C3. Cross those squares out.
  7. Wherever the cat in the Blue region ends up, it rules out R2C8 and R2C9. Cross those squares out.
  8. Wherever the cat in the Pink region ends up, it rules out R4C7. Cross that square out.
  9. Wherever the cat in row 2 ends up, it rules out R1C2, R1C3 and R3C2. Cross those squares out.
  10. The Yellow, Blue and Pink regions can only use columns 7, 8 and 9, so columns 7, 8 and 9 are already spoken for. Cross out R1C7, R2C7, R3C7 and R6C7.
  11. Wherever the cat in column 7 ends up, it rules out R5C9 and R6C6. Cross those squares out.
  12. The Yellow and Green regions can only use rows 6 and 7, so rows 6 and 7 are already spoken for. Cross out R6C2, R7C2 and R7C3.
  13. Wherever the cat in the Teal region ends up, it rules out R5C7. Cross that square out.
  14. Column 7 has only one open square left: R7C7. Put a cat there.
  15. The Orange region has only one open square left: R8C5. Put a cat there.
  16. The Green region has only one open square left: R6C4. Put a cat there.
  17. Wherever the cat in the Red region ends up, it rules out R5C2. Cross that square out.
  18. Wherever the cat in the Teal region ends up, it rules out R1C6, R2C6 and R3C6. Cross those squares out.
  19. The Grey region has only one open square left: R2C3. Put a cat there.
  20. The Red region has only one open square left: R4C2. Put a cat there.
  21. The Teal region has only one open square left: R5C6. Put a cat there.
  22. The Pink region has only one open square left: R3C8. Put a cat there.
  23. The Blue region has only one open square left: R1C9. 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 19 squares. It can be solved in 23 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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