GridMew1Exclude common neighbors
The cat in row 3 must occupy one of row 3, column 1; row 3, column 2; row 3, column 3. Each of row 2, 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-5-0012
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 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 4 forced placements and 4 candidate-elimination steps after the givens. Region sizes: A: 2 · B: 6 · C: 7 · D: 6 · E: 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
2Use a candidate lock
Every candidate in column 1 lies in region C (row 1, column 1; row 2, column 1; row 3, column 1; row 5, column 1). Its cat must use that shared section. Exclude row 3, column 2 from the rest of region C.
Before step 2. Exclude 1 cells; then scan for a new single.3Use a candidate lock
Every candidate in column 4 lies in region B (row 1, column 4; row 2, column 4). Its cat must use that shared section. Exclude row 2, column 3 from the rest of region B.
Before step 3. Exclude 1 cells; then scan for a new single.4Exclude common neighbors
The cat in column 4 must occupy one of row 1, column 4; row 2, column 4. Each of row 1, column 3 touches every candidate, so none can hold a cat.
Before step 4. Exclude 1 cells; then scan for a new single.5Check region A
region A has only one remaining candidate: row 1, column 2. Every other cell is excluded by earlier placements or deductions. Place the cat here.
Before step 5. Place one cat, then exclude 4 other cells.6Check row 2
row 2 has only one remaining candidate: row 2, column 4. 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 3
row 3 has only one remaining candidate: row 3, column 1. 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 3. Every other cell is excluded by earlier placements or deductions. Place the cat here.
Before step 8. 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: r1c2, r2c4, r3c1, r4c5, r5c3.