6 × 6 challenge
Try the puzzle yourself, then explore how the deductions build.
This original 6×6 board has 6 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 5 forced placements and 3 candidate-elimination steps after the givens. Region sizes: A: 2 · B: 13 · C: 7 · D: 2 · E: 10 · 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.
Every candidate in row 2 lies in region B (row 2, column 1; row 2, column 2; row 2, column 3; row 2, column 4). Its cat must use that shared section. Exclude row 3, column 3; row 3, column 4; row 3, column 5 from the rest of region B.
Before step 1. Exclude 3 cells; then scan for a new single.Every candidate in row 3 lies in region C (row 3, column 1; row 3, column 2). Its cat must use that shared section. Exclude row 4, column 1; row 4, column 2; row 5, column 1; row 5, column 2; row 6, column 1 from the rest of region C.
Before step 2. Exclude 5 cells; then scan for a new single.The cat in row 3 must occupy one of row 3, column 1; row 3, column 2. Each of row 2, column 1; row 2, column 2 touches every candidate, so none can hold a cat.
Before step 3. Exclude 2 cells; then scan for a new single.column 1 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 4. Place one cat, then exclude 1 other cells.column 2 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 5. Place one cat, then exclude 4 other cells.region D 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 6. Place one cat, then exclude 4 other cells.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 7. Place one cat, then exclude 0 other cells.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 0 other cells.The final cats satisfy every row, column and region quota, with no edge or corner contact.
Cat positions: r1c6, r2c4, r3c1, r4c3, r5c5, r6c2.
GridMew