Puzzle gm-8-0005

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 2 fixed cats. The smallest region is A, with 4 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 6 forced placements and 5 candidate-elimination steps after the givens. Region sizes: A: 4 · B: 4 · C: 4 · D: 9 · E: 24 · F: 8 · G: 7 · H: 4. 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 column 5 lies in region E (row 1, column 5; row 2, column 5; row 3, column 5; row 4, column 5; row 5, column 5). Its cat must use that shared section. Exclude row 1, column 4; row 1, column 7; row 2, column 7; row 3, column 7; row 4, column 1; row 4, column 2; row 4, column 4; row 5, column 2; row 5, column 3; row 5, column 4; row 6, column 3; row 6, column 4 from the rest of region E.

Before step 1. Exclude 12 cells; then scan for a new single.

2Use a candidate lock

Every candidate in row 6 lies in region F (row 6, column 1; row 6, column 2). Its cat must use that shared section. Exclude row 5, column 1 from the rest of region F.

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

3Use a candidate lock

Every candidate in column 4 lies in region C (row 2, column 4; row 3, column 4). Its cat must use that shared section. Exclude row 3, column 3; row 4, column 3 from the rest of region C.

Before step 3. Exclude 2 cells; then scan for a new single.

4Use a candidate lock

Every candidate in column 3 lies in region A (row 1, column 3; row 2, column 3). Its cat must use that shared section. Exclude row 1, column 1; row 1, column 2 from the rest of region A.

Before step 4. Exclude 2 cells; then scan for a new single.

5Exclude common neighbors

The cat in row 1 must occupy one of row 1, column 3; row 1, column 5. Each of row 2, column 4 touches every candidate, so none can hold a cat.

Before step 5. Exclude 1 cells; then scan for a new single.

6Check column 4

column 4 has only one remaining candidate: row 3, column 4. Every other cell is excluded by earlier placements or deductions. Place the cat here.

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

7Check row 4

row 4 has only one remaining candidate: row 4, column 7. Every other cell is excluded by earlier placements or deductions. Place the cat here.

Before step 7. Place one cat, then exclude 1 other cells.

8Check row 5

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

Before step 8. Place one cat, then exclude 1 other cells.

9Check row 1

row 1 has only one remaining candidate: row 1, column 3. Every other cell is excluded by earlier placements or deductions. Place the cat here.

Before step 9. Place one cat, then exclude 1 other cells.

10Check row 2

row 2 has only one remaining candidate: row 2, column 1. Every other cell is excluded by earlier placements or deductions. Place the cat here.

Before step 10. Place one cat, then exclude 1 other cells.

11Check row 6

row 6 has only one remaining candidate: row 6, column 2. Every other cell is excluded by earlier placements or deductions. Place the cat here.

Before step 11. 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: r1c3, r2c1, r3c4, r4c7, r5c5, r6c2, r7c6, r8c8.