Puzzle gm-8-0002

8 × 8 challenge

Take this puzzle one clear step at a time.

Try the puzzle yourself, then explore how the deductions build.

Puzzle board · starting state

Your starting point

This original 8×8 board has 8 connected regions and 3 fixed cats. The smallest region is F, with 5 cells. Start by ruling out every other cell in each fixed cat’s row, column and region, plus its immediate neighbors.

The verified route below uses 5 forced placements and 1 candidate-elimination step after the givens. Region sizes: A: 6 · B: 6 · C: 15 · D: 8 · E: 13 · F: 5 · G: 5 · H: 6. These are observations about this board, not a guarantee that a smaller region always contains the next move.

Read each diagram in sequence. Cats and × marks in the before-state come from earlier deductions. Green outlines identify the current observation. Open the final answer only when you want the spoiler.

Step-by-step walkthrough

1Use a candidate lock

Every candidate in row 5 lies in region E (row 5, column 6; row 5, column 8). Its cat must use that shared section. Exclude row 4, column 6; row 4, column 8 from the rest of region E.

Before step 1. Exclude 2 cells; then scan for a new single.

2Check row 4

row 4 has only one remaining candidate: row 4, column 5. Every other cell is excluded by earlier placements or deductions. Place the cat here.

Before step 2. Place one cat, then exclude 4 other cells.

3Check row 5

row 5 has only one remaining candidate: row 5, column 8. Every other cell is excluded by earlier placements or deductions. Place the cat here.

Before step 3. Place one cat, then exclude 2 other cells.

4Check row 2

row 2 has only one remaining candidate: row 2, column 3. Every other cell is excluded by earlier placements or deductions. Place the cat here.

Before step 4. Place one cat, then exclude 3 other cells.

5Check row 1

row 1 has only one remaining candidate: row 1, column 6. Every other cell is excluded by earlier placements or deductions. Place the cat here.

Before step 5. Place one cat, then exclude 0 other cells.

6Check row 8

row 8 has only one remaining candidate: row 8, column 2. Every other cell is excluded by earlier placements or deductions. Place the cat here.

Before step 6. Place one cat, then exclude 0 other cells.

Show solution · reveals all cat positions

The final cats satisfy every row, column and region quota, with no edge or corner contact.

Cat positions: r1c6, r2c3, r3c1, r4c5, r5c8, r6c4, r7c7, r8c2.