Find the Cat #297: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (14)Orange (13)Yellow (1)Green (17)Teal (8)Blue (6)Purple (7)Pink (8)Brown (17)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 Yellow region has only one open square left: R1C10. Put a cat there.
  2. The Teal region has only one open square left: R8C9. Put a cat there.
  3. Wherever the cat in the Purple region ends up, it rules out R9C6. Cross that square out.
  4. The Orange and Pink regions can only use rows 9 and 10, so rows 9 and 10 are already spoken for. Cross out R9C3, R9C4 and R9C5.
  5. The Purple region has only one open square left: R7C6. Put a cat there.
  6. The Blue region has only one open square left: R6C1. Put a cat there.
  7. The Grey region has only one open square left: R3C2. Put a cat there.
  8. The Pink region has only one open square left: R10C3. Put a cat there.
  9. The Orange region has only one open square left: R9C7. Put a cat there.
  10. Wherever the cat in the Red region ends up, it rules out R2C8 and R4C5. Cross those squares out.
  11. The Green region has only one open square left: R5C8. Put a cat there.
  12. The Red region has only one open square left: R2C5. Put a cat there.
  13. The Brown region has only one open square left: R4C4. Put a cat there.

About this puzzle

Where to start: the Yellow region is a single square, so its cat is already decided. Its 10 color regions range from 1 square (Yellow) to 17 squares. It can be solved in 13 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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