Puzzle gm-8-0007

8 × 8 intro

Take this puzzle one clear step at a time.

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

Puzzle board · starting state

gm-8-0007: 8×8 regional boardCCAAABBBCCADDBBBCCCDDDDBCCEDDDDBEEEEEDDDEFEEEDDDEEHHGGDDHHHHGGDD

Your starting point

This original 8×8 board has 8 connected regions and 2 fixed cats. The smallest region is F, with 1 cell. 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 6 forced placements and 0 candidate-elimination steps after the givens. Region sizes: A: 4 · B: 8 · C: 9 · D: 20 · E: 12 · F: 1 · G: 4 · H: 6. 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 F

region F has only one remaining candidate: row 6, column 2. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-8-0007: 8×8 regional boardC×C×AA×ABBBC×C×AD×DBBBCC×C×D×D×D×D×B×C×C×E×D×D×DDBE×E×E×EE×D×D×D×E×FE×E×E×DDDE×E×HH×GGDDH×HHH×GGDDBefore step 1. Place one cat, then exclude 5 other cells.

2Check region H

region H has only one remaining candidate: row 8, column 3. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-8-0007: 8×8 regional boardC×C×AA×ABBBC×C×AD×DBBBCC×C×D×D×D×D×B×C×C×E×D×D×DDBE×E×E×EE×D×D×D×E×FE×E×E×D×D×D×E×E×H×H×GGDDH×H×HH×GGDDBefore step 2. Place one cat, then exclude 6 other cells.

3Check region A

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

gm-8-0007: 8×8 regional boardC×C×A×A×ABBBC×C×A×D×DBBBCC×C×D×D×D×D×B×C×C×E×D×D×DDBE×E×E×EE×D×D×D×E×FE×E×E×D×D×D×E×E×H×H×GGDDH×H×HH×G×G×D×D×Before step 3. Place one cat, then exclude 6 other cells.

4Check region G

region G has only one remaining candidate: row 7, column 6. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-8-0007: 8×8 regional boardC×C×A×A×AB×B×B×C×C×A×D×D×B×BBCC×C×D×D×D×D×B×C×C×E×D×D×DDBE×E×E×EE×D×D×D×E×FE×E×E×D×D×D×E×E×H×H×G×GDDH×H×HH×G×G×D×D×Before step 4. Place one cat, then exclude 3 other cells.

5Check region D

region D has only one remaining candidate: row 4, column 7. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-8-0007: 8×8 regional boardC×C×A×A×AB×B×B×C×C×A×D×D×B×BBCC×C×D×D×D×D×B×C×C×E×D×D×D×DBE×E×E×EE×D×D×D×E×FE×E×E×D×D×D×E×E×H×H×G×GD×D×H×H×HH×G×G×D×D×Before step 5. Place one cat, then exclude 2 other cells.

6Check row 2

row 2 has only one remaining candidate: row 2, column 8. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-8-0007: 8×8 regional boardC×C×A×A×AB×B×B×C×C×A×D×D×B×B×BCC×C×D×D×D×D×B×C×C×E×D×D×D×DB×E×E×E×EE×D×D×D×E×FE×E×E×D×D×D×E×E×H×H×G×GD×D×H×H×HH×G×G×D×D×Before step 6. 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-8-0007: 8×8 regional boardCCAAABBBCCADDBBBCCCDDDDBCCEDDDDBEEEEEDDDEFEEEDDDEEHHGGDDHHHHGGDD

Cat positions: r1c5, r2c8, r3c1, r4c7, r5c4, r6c2, r7c6, r8c3.

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How this puzzle and its reasoning are verified