Puzzle gm-8-0006

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-8-0006: 8×8 regional boardAACBBBBBCCCBBBBBCCCBBEBEGCDDDEEEGGGEEEEEGGGGEFFEGGGGFFFHGGGGGGHH

Your starting point

This original 8×8 board has 8 connected regions and 3 fixed cats. 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 0 candidate-elimination steps after the givens. Region sizes: A: 2 · B: 13 · C: 8 · D: 3 · E: 12 · F: 5 · G: 18 · H: 3. 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 row 6

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

gm-8-0006: 8×8 regional boardA×AC×B×B×B×B×B×C×C×C×B×BBBB×CC×CB×BE×BE×G×C×DD×DE×E×E×G×G×G×E×E×E×E×EG×G×G×G×E×FF×E×G×G×G×GF×F×F×H×G×G×G×G×G×G×HH×Before step 1. Place one cat, then exclude 1 other cells.

2Check row 8

row 8 has only one remaining candidate: row 8, column 7. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-8-0006: 8×8 regional boardA×AC×B×B×B×B×B×C×C×C×B×BB×BB×CC×CB×BE×BE×G×C×DD×DE×E×E×G×G×G×E×E×E×E×EG×G×G×G×E×FF×E×G×G×G×GF×F×F×H×G×G×G×G×G×G×HH×Before step 2. Place one cat, then exclude 2 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-8-0006: 8×8 regional boardA×AC×B×B×B×B×B×C×C×C×B×BB×B×B×CC×CB×BE×B×E×G×C×DD×DE×E×E×G×G×G×E×E×E×E×EG×G×G×G×E×FF×E×G×G×G×GF×F×F×H×G×G×G×G×G×G×HH×Before step 3. Place one cat, then exclude 2 other cells.

4Check row 4

row 4 has only one remaining candidate: row 4, column 3. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-8-0006: 8×8 regional boardA×AC×B×B×B×B×B×C×C×C×B×BB×B×B×CC×CB×B×E×B×E×G×C×DD×D×E×E×E×G×G×G×E×E×E×E×EG×G×G×G×E×FF×E×G×G×G×GF×F×F×H×G×G×G×G×G×G×HH×Before step 4. Place one cat, then exclude 1 other cells.

5Check row 3

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

gm-8-0006: 8×8 regional boardA×AC×B×B×B×B×B×C×C×C×B×BB×B×B×CC×C×B×B×E×B×E×G×C×DD×D×E×E×E×G×G×G×E×E×E×E×EG×G×G×G×E×FF×E×G×G×G×GF×F×F×H×G×G×G×G×G×G×HH×Before 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-8-0006: 8×8 regional boardAACBBBBBCCCBBBBBCCCBBEBEGCDDDEEEGGGEEEEEGGGGEFFEGGGGFFFHGGGGGGHH

Cat positions: r1c2, r2c5, r3c1, r4c3, r5c8, r6c6, r7c4, r8c7.

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How this puzzle and its reasoning are verified