Puzzle gm-8-0010

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-8-0010: 8×8 regional boardCCCAABBBCCCACCBBDCCCCCCCDDDCEEEEDDGGEEEEDFGGGHHHFFFGGGHHFFFGGGHH

Your starting point

This original 8×8 board has 8 connected regions and 3 fixed cats. The smallest region is A, with 3 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 0 candidate-elimination steps after the givens. Region sizes: A: 3 · B: 5 · C: 16 · D: 7 · E: 8 · F: 7 · G: 11 · H: 7. 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 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-8-0010: 8×8 regional boardCC×CA×ABBB×CC×CA×CCBB×DC×CC×CCCC×DD×DC×EEEE×D×D×G×G×EEEE×D×FG×G×G×H×H×H×F×F×F×GG×G×H×H×F×F×F×G×G×G×H×HBefore step 1. Place one cat, then exclude 9 other cells.

2Check region B

region B has only one remaining candidate: row 2, column 7. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-8-0010: 8×8 regional boardC×C×C×A×AB×B×B×CC×CA×C×C×BB×DC×CC×C×CCC×DD×DC×E×EEE×D×D×G×G×E×EEE×D×FG×G×G×H×H×H×F×F×F×GG×G×H×H×F×F×F×G×G×G×H×HBefore step 2. Place one cat, then exclude 6 other cells.

3Check row 5

row 5 has only one remaining candidate: row 5, column 6. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-8-0010: 8×8 regional boardC×C×C×A×AB×B×B×C×C×C×A×C×C×BB×DC×CC×C×C×C×C×DD×DC×E×EE×E×D×D×G×G×E×EE×E×D×FG×G×G×H×H×H×F×F×F×GG×G×H×H×F×F×F×G×G×G×H×HBefore step 3. Place one cat, then exclude 1 other cells.

4Check region C

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

gm-8-0010: 8×8 regional boardC×C×C×A×AB×B×B×C×C×C×A×C×C×BB×DC×CC×C×C×C×C×DD×DC×E×E×E×E×D×D×G×G×E×EE×E×D×FG×G×G×H×H×H×F×F×F×GG×G×H×H×F×F×F×G×G×G×H×HBefore step 4. Place one cat, then exclude 2 other cells.

5Check row 4

row 4 has only one remaining candidate: row 4, column 1. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-8-0010: 8×8 regional boardC×C×C×A×AB×B×B×C×C×C×A×C×C×BB×D×C×CC×C×C×C×C×DD×D×C×E×E×E×E×D×D×G×G×E×EE×E×D×FG×G×G×H×H×H×F×F×F×GG×G×H×H×F×F×F×G×G×G×H×HBefore step 5. 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-8-0010: 8×8 regional boardCCCAABBBCCCACCBBDCCCCCCCDDDCEEEEDDGGEEEEDFGGGHHHFFFGGGHHFFFGGGHH

Cat positions: r1c5, r2c7, r3c3, r4c1, r5c6, r6c2, r7c4, r8c8.

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How this puzzle and its reasoning are verified