Puzzle gm-6-0012

6 × 6 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 6×6 board has 6 connected regions and 1 fixed cat. The smallest region is F, with 2 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 2 candidate-elimination steps after the givens. Region sizes: A: 8 · B: 3 · C: 7 · D: 10 · E: 6 · F: 2. 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

1Check region B

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

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

2Use a candidate lock

Every candidate in row 3 lies in region C (row 3, column 4; row 3, column 5; row 3, column 6). Its cat must use that shared section. Exclude row 1, column 6; row 4, column 6; row 5, column 6 from the rest of region C.

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

3Check column 6

column 6 has only one remaining candidate: row 3, column 6. Every other cell is excluded by earlier placements or deductions. Place the cat here.

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

4Use a candidate lock

Every candidate in row 4 lies in region D (row 4, column 3; row 4, column 4). Its cat must use that shared section. Exclude row 5, column 3 from the rest of region D.

Before step 4. Exclude 1 cells; then scan for a new single.

5Check column 3

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

Before step 5. Place one cat, then exclude 2 other cells.

6Check 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 6. Place one cat, then exclude 1 other cells.

7Check row 1

row 1 has only one remaining candidate: row 1, column 4. Every other cell is excluded by earlier placements or deductions. Place the cat here.

Before step 7. 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: r1c4, r2c2, r3c6, r4c3, r5c5, r6c1.