Find the Cat #261: 10x10 Grid Puzzle (Hard)

hard

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

0 / 10 cats · 0:00
Red (1)Orange (8)Yellow (12)Green (10)Teal (10)Blue (7)Purple (7)Pink (7)Brown (17)Grey (21)

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: R10C1. Put a cat there.
  2. The Green region has only one open square left: R9C3. Put a cat there.
  3. The Teal region has only one open square left: R8C9. Put a cat there.
  4. The Orange, Blue, Purple and Pink regions can only use rows 1, 2, 3 and 4, so rows 1, 2, 3 and 4 are already spoken for. Cross out R2C2, R3C2, R4C2, R4C6, R4C7 and R4C8.
  5. Wherever the cat in the Yellow region ends up, it rules out R5C5, R5C6, R5C7, R5C8 and R5C10. Cross those squares out.
  6. The Orange and Yellow regions can only use columns 2 and 4, so columns 2 and 4 are already spoken for. Cross out R4C4, R6C2, R6C4, R7C2 and R7C4.
  7. The Brown region has only one open square left: R6C5. Put a cat there.
  8. The Yellow region has only one open square left: R5C2. Put a cat there.
  9. The Grey region has only one open square left: R7C7. Put a cat there.
  10. The Purple region has only one open square left: R3C6. Put a cat there.
  11. Row 4 has only one open square left: R4C10. Put a cat there.
  12. The Blue region has only one open square left: R1C8. Put a cat there.
  13. The Orange region has only one open square left: R2C4. 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 21 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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