Puzzle gm-6-0007

6 × 6 challenge

Take this puzzle one clear step at a time.

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

Puzzle board · starting state

gm-6-0007: 6×6 regional boardBBBAAABBBCCCBBBCCCBBDDCCEBBBCCEFFFCC

Your starting point

This original 6×6 board has 6 connected regions and 2 fixed cats. The smallest region is D, 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 1 candidate-elimination step after the givens. Region sizes: A: 3 · B: 14 · C: 12 · D: 2 · E: 2 · F: 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 region F

region F has only one remaining candidate: row 6, column 3. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-6-0007: 6×6 regional boardB×BBA×AAB×BBC×CCB×BB×C×C×CB×B×D×DC×C×EB×B×B×C×C×E×F×FF×CCBefore step 1. Place one cat, then exclude 4 other cells.

2Exclude common neighbors

The cat in column 5 must occupy one of row 1, column 5; row 2, column 5. Each of row 1, column 6; row 2, column 6 touches every candidate, so none can hold a cat.

gm-6-0007: 6×6 regional boardB×BB×A×AAB×BB×C×CCB×BB×C×C×CB×B×D×DC×C×EB×B×B×C×C×E×F×FF×C×C×Before step 2. Exclude 2 cells; then scan for a new single.

3Check column 6

column 6 has only one remaining candidate: row 3, column 6. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-6-0007: 6×6 regional boardB×BB×A×AA×B×BB×C×CC×B×BB×C×C×CB×B×D×DC×C×EB×B×B×C×C×E×F×FF×C×C×Before step 3. Place one cat, then exclude 2 other cells.

4Check row 2

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

gm-6-0007: 6×6 regional boardB×BB×A×AA×B×BB×C×C×C×B×B×B×C×C×CB×B×D×DC×C×EB×B×B×C×C×E×F×FF×C×C×Before step 4. Place one cat, then exclude 1 other cells.

5Check row 1

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

gm-6-0007: 6×6 regional boardB×B×B×A×AA×B×BB×C×C×C×B×B×B×C×C×CB×B×D×DC×C×EB×B×B×C×C×E×F×FF×C×C×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-6-0007: 6×6 regional boardBBBAAABBBCCCBBBCCCBBDDCCEBBBCCEFFFCC

Cat positions: r1c5, r2c2, r3c6, r4c4, r5c1, r6c3.

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How this puzzle and its reasoning are verified