GridMew1Exclude common neighbors
The cat in row 2 must occupy one of row 2, column 1; row 2, column 2; row 2, column 3. Each of row 3, column 2 touches every candidate, so none can hold a cat.
Before step 1. Exclude 1 cells; then scan for a new single.Keep several possibilities alive while locks accumulate
Original puzzle gm-5-0003
By GridMew · Published 15 October 2026 · Updated 16 October 2026
5 × 5 challenge
Read the starting position, follow the deductions, and check the move that is easy to misread.
Puzzle board · starting state
How to approach this board
Coordinates such as r2c3 mean row 2, column 3. Count rows from the top and columns from the left.
The top-right given does not produce an immediate single. This board rewards patient exclusions: row 2, column 4 and the bottom region each provide information while their own cat positions remain unsettled.
5×5 · 1 fixed cats · 11 explained deductions. Region sizes: A: 3 · B: 6 · C: 9 · D: 4 · E: 3.
A deduction worth checking
Region E has candidates r5c3 and r5c4, both in row 5. That reserves the row for E and removes r5c1 and r5c2; it does not choose between the two E cells.
A move to double-check · r3c3
Before step 7, column 2 can use r2c2 or r4c2. Both touch r3c3. The two candidates are separated, so a shared-neighbor exclusion need not come from adjacent candidate cells.
Green marks the cell being discussed, not a cat to place. This is the position before step 7; 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.
B B C A A B B C C A B B C C C D D C C C D D E E E
Fixed cats: row 1, column 5. One cat is required in each row, column and region.
Step-by-step walkthrough
2Exclude common neighbors
The cat in column 4 must occupy one of row 3, column 4; row 4, column 4; row 5, column 4. Each of row 4, column 3 touches every candidate, so none can hold a cat.
Before step 2. Exclude 1 cells; then scan for a new single.3Use a candidate lock
Every candidate in region E lies in row 5 (row 5, column 3; row 5, column 4). Its cat must use that shared section. Exclude row 5, column 1; row 5, column 2 from the rest of row 5.
Before step 3. Exclude 2 cells; then scan for a new single.4Exclude common neighbors
The cat in row 5 must occupy one of row 5, column 3; row 5, column 4. Each of row 4, column 4 touches every candidate, so none can hold a cat.
Before step 4. Exclude 1 cells; then scan for a new single.5Exclude common neighbors
The cat in row 4 must occupy one of row 4, column 1; row 4, column 2. Each of row 3, column 1 touches every candidate, so none can hold a cat.
Before step 5. Exclude 1 cells; then scan for a new single.6Use a candidate lock
Every candidate in row 3 lies in region C (row 3, column 3; row 3, column 4). Its cat must use that shared section. Exclude row 2, column 3 from the rest of region C.
Before step 6. Exclude 1 cells; then scan for a new single.7Exclude common neighbors
The cat in column 2 must occupy one of row 2, column 2; row 4, column 2. Each of row 3, column 3 touches every candidate, so none can hold a cat.
Before step 7. Exclude 1 cells; then scan for a new single.8Check row 3
row 3 has only one remaining candidate: row 3, column 4. Every other cell is excluded by earlier placements or deductions. Place the cat here.
Before step 8. Place one cat, then exclude 1 other cells.9Check row 5
row 5 has only one remaining candidate: row 5, column 3. Every other cell is excluded by earlier placements or deductions. Place the cat here.
Before step 9. Place one cat, then exclude 1 other cells.10Check 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.
Before step 10. Place one cat, then exclude 1 other cells.11Check 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.
Before step 11. 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.
Cat positions: r1c5, r2c2, r3c4, r4c1, r5c3.
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