Puzzle gm-5-0008

5 × 5 practice

Take this puzzle one clear step at a time.

Try the puzzle yourself, then explore how the deductions build.

Puzzle board · starting state

gm-5-0008: 5×5 regional boardCAADBCAADBCCCDDECDDDECDDD

Your starting point

This original 5×5 board has 5 connected regions and 1 fixed cat. The smallest region is B, 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 0 candidate-elimination steps after the givens. Region sizes: A: 4 · B: 2 · C: 7 · D: 10 · E: 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 E

region E has only one remaining candidate: row 5, column 1. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-5-0008: 5×5 regional boardCAAD×BCAAD×BCCC×D×D×E×C×D×DD×ECD×D×D×Before step 1. Place one cat, then exclude 4 other cells.

2Check row 3

row 3 has only one remaining candidate: row 3, column 2. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-5-0008: 5×5 regional boardC×AAD×BC×AAD×BC×CC×D×D×E×C×D×DD×EC×D×D×D×Before step 2. Place one cat, then exclude 3 other cells.

3Check row 2

row 2 has only one remaining candidate: row 2, column 5. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-5-0008: 5×5 regional boardC×A×AD×BC×A×A×D×BC×CC×D×D×E×C×D×DD×EC×D×D×D×Before step 3. Place one cat, then exclude 1 other cells.

4Check row 1

row 1 has only one remaining candidate: row 1, column 3. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-5-0008: 5×5 regional boardC×A×AD×B×C×A×A×D×BC×CC×D×D×E×C×D×DD×EC×D×D×D×Before step 4. 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.

gm-5-0008: 5×5 regional boardCAADBCAADBCCCDDECDDDECDDD

Cat positions: r1c3, r2c5, r3c2, r4c4, r5c1.

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How this puzzle and its reasoning are verified