GridMew1Exclude common neighbors
The cat in row 2 must occupy one of row 2, column 1; row 2, column 2; row 2, column 3. Each of row 3, column 2 touches every candidate, so none can hold a cat.
Before step 1. Exclude 1 cells; then scan for a new single.Puzzle gm-5-0003
5 × 5 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 5×5 board has 5 connected regions and 1 fixed cat. The smallest region is A, with 3 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 4 forced placements and 7 candidate-elimination steps after the givens. Region sizes: A: 3 · B: 6 · C: 9 · D: 4 · E: 3. 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
2Exclude common neighbors
The cat in column 4 must occupy one of row 3, column 4; row 4, column 4; row 5, column 4. Each of row 4, column 3 touches every candidate, so none can hold a cat.
Before step 2. Exclude 1 cells; then scan for a new single.3Use a candidate lock
Every candidate in region E lies in row 5 (row 5, column 3; row 5, column 4). Its cat must use that shared section. Exclude row 5, column 1; row 5, column 2 from the rest of row 5.
Before step 3. Exclude 2 cells; then scan for a new single.4Exclude common neighbors
The cat in row 5 must occupy one of row 5, column 3; row 5, column 4. Each of row 4, column 4 touches every candidate, so none can hold a cat.
Before step 4. Exclude 1 cells; then scan for a new single.5Exclude common neighbors
The cat in row 4 must occupy one of row 4, column 1; row 4, column 2. Each of row 3, column 1 touches every candidate, so none can hold a cat.
Before step 5. Exclude 1 cells; then scan for a new single.6Use a candidate lock
Every candidate in row 3 lies in region C (row 3, column 3; row 3, column 4). Its cat must use that shared section. Exclude row 2, column 3 from the rest of region C.
Before step 6. Exclude 1 cells; then scan for a new single.7Exclude common neighbors
The cat in column 2 must occupy one of row 2, column 2; row 4, column 2. Each of row 3, column 3 touches every candidate, so none can hold a cat.
Before step 7. Exclude 1 cells; then scan for a new single.8Check row 3
row 3 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 8. Place one cat, then exclude 1 other cells.9Check row 5
row 5 has only one remaining candidate: row 5, 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 4
row 4 has only one remaining candidate: row 4, 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 2
row 2 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 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: r1c5, r2c2, r3c4, r4c1, r5c3.