Two singleton regions set up a vertical lock

Original puzzle gm-6-0003

By GridMew · Published 15 October 2026 · Updated 16 October 2026

6 × 6 challenge

Read the starting position, follow the deductions, and check the move that is easy to misread.

Puzzle board · starting state

gm-6-0003: 6×6 regional boardAABBBBAABBBBDDCBBBDEEEEEDEEEEEDEEEEF

How to approach this board

Coordinates such as r2c3 mean row 2, column 3. Count rows from the top and columns from the left.

There are no givens. Regions C and F each contain one cell, at r3c3 and r6c6. After those forced cats, D still has a choice of rows, but both candidates occupy the leftmost column.

6×6 · 0 fixed cats · 7 explained deductions. Region sizes: A: 4 · B: 11 · C: 1 · D: 5 · E: 14 · F: 1.

A deduction worth checking

D can use r4c1 or r5c1. It therefore takes column 1’s cat, excluding r1c1 and r2c1 and leaving row 2 to resolve elsewhere.

gm-6-0003: 6×6 regional boardAAB×BBB×AA×B×B×BB×D×D×CB×B×B×DE×E×E×EE×DEE×EE×E×D×E×E×E×E×F
Position before step 3. Review the technique.
A move to double-check · r2c1

Choosing the upper or lower D cell is unnecessary. Either choice would prevent r2c1, because column 1 can contain only one cat.

gm-6-0003: 6×6 regional boardAAB×BBB×AA×B×B×BB×D×D×CB×B×B×DE×E×E×EE×DEE×EE×E×D×E×E×E×E×F

Green marks the cell being discussed, not a cat to place. This is the position before step 3; compare the deduction below.

Read the starting board as text

Each line is one row, left to right. Matching letters belong to the same connected region.

A A B B B B
A A B B B B
D D C B B B
D E E E E E
D E E E E E
D E E E E F

Fixed cats: none. One cat is required in each row, column and region.

Step-by-step walkthrough

1Check 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-6-0003: 6×6 regional boardAABBBBAABBBBDDCBBBDEEEEEDEEEEEDEEEEFBefore step 1. Place one cat, then exclude 14 other cells.

2Check region F

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

gm-6-0003: 6×6 regional boardAAB×BBBAA×B×B×BBD×D×CB×B×B×DE×E×E×EEDEE×EEEDEE×EEFBefore step 2. Place one cat, then exclude 9 other cells.

3Use a candidate lock

Every candidate in region D lies in column 1 (row 4, column 1; row 5, column 1). Its cat must use that shared section. Exclude row 1, column 1; row 2, column 1 from the rest of column 1.

gm-6-0003: 6×6 regional boardAAB×BBB×AA×B×B×BB×D×D×CB×B×B×DE×E×E×EE×DEE×EE×E×D×E×E×E×E×FBefore step 3. Exclude 2 cells; then scan for a new single.

4Check 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-6-0003: 6×6 regional boardA×AB×BBB×A×A×B×B×BB×D×D×CB×B×B×DE×E×E×EE×DEE×EE×E×D×E×E×E×E×FBefore step 4. Place one cat, then exclude 3 other cells.

5Check row 1

row 1 has only one remaining candidate: row 1, column 2. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-6-0003: 6×6 regional boardA×AB×B×B×B×A×A×B×B×BB×D×D×CB×B×B×DE×E×E×E×E×DEE×EE×E×D×E×E×E×E×FBefore step 5. Place one cat, then exclude 1 other cells.

6Check 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-6-0003: 6×6 regional boardA×AB×B×B×B×A×A×B×B×BB×D×D×CB×B×B×DE×E×E×E×E×DE×E×EE×E×D×E×E×E×E×FBefore step 6. Place one cat, then exclude 1 other cells.

7Check row 5

row 5 has only one remaining candidate: row 5, column 4. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-6-0003: 6×6 regional boardA×AB×B×B×B×A×A×B×B×BB×D×D×CB×B×B×DE×E×E×E×E×D×E×E×EE×E×D×E×E×E×E×FBefore step 7. 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-6-0003: 6×6 regional boardAABBBBAABBBBDDCBBBDEEEEEDEEEEEDEEEEF

Cat positions: r1c2, r2c5, r3c3, r4c1, r5c4, r6c6.

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How this puzzle and its reasoning are verified