5 × 5 challenge
Try the puzzle yourself, then explore how the deductions build.
This original 5×5 board has 5 connected regions and 0 fixed cats. The smallest region is C, 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 3 candidate-elimination steps after the givens. Region sizes: A: 5 · B: 9 · C: 2 · D: 5 · 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.
Every candidate in column 1 lies in region B (row 1, column 1; row 2, column 1; row 3, column 1; row 4, column 1; row 5, column 1). Its cat must use that shared section. Exclude row 1, column 2; row 1, column 3; row 2, column 2; row 2, column 3 from the rest of region B.
Before step 1. Exclude 4 cells; then scan for a new single.Every candidate in column 2 lies in region E (row 3, column 2; row 4, column 2; row 5, column 2). Its cat must use that shared section. Exclude row 5, column 3 from the rest of region E.
Before step 2. Exclude 1 cells; then scan for a new single.The cat in column 2 must occupy one of row 3, column 2; row 4, column 2; row 5, column 2. Each of row 4, column 1; row 4, column 3 touches every candidate, so none can hold a cat.
Before step 3. Exclude 2 cells; then scan for a new single.column 3 has only one remaining candidate: row 3, column 3. Every other cell is excluded by earlier placements or deductions. Place the cat here.
Before step 4. Place one cat, then exclude 7 other cells.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 5. Place one cat, then exclude 4 other cells.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 6. Place one cat, then exclude 2 other cells.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.row 5 has only one remaining candidate: row 5, column 2. 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.The final cats satisfy every row, column and region quota, with no edge or corner contact.
Cat positions: r1c4, r2c1, r3c3, r4c5, r5c2.
GridMew