Original puzzle gm-5-0005
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.
Coordinates such as r2c3 mean row 2, column 3. Count rows from the top and columns from the left.
There are no fixed cats, yet the first column is entirely region B. Its required cat therefore satisfies B as well. Work from that relationship rather than choosing an attractive corner.
5×5 · 0 fixed cats · 8 explained deductions. Region sizes: A: 5 · B: 9 · C: 2 · D: 5 · E: 4.
After two locks and a common-neighbor exclusion, column 3 has just r3c3. The preceding steps establish that single; the shape of region C alone does not.
r1c2 is inside B but outside column 1. Placing B there would leave column 1 unable to contain its own cat without giving B a second one.
Green marks the cell being discussed, not a cat to place. This is the position before step 1; compare the deduction below.
Each line is one row, left to right. Matching letters belong to the same connected region.
B B B A A B B B A A B E C C A B E D D D B E E D D
Fixed cats: none. One cat is required in each row, column and region.
Every candidate in column 1 lies in region B (row 1, column 1; row 2, column 1; row 3, column 1; row 4, column 1; row 5, column 1). Its cat must use that shared section. Exclude row 1, column 2; row 1, column 3; row 2, column 2; row 2, column 3 from the rest of region B.
Before step 1. Exclude 4 cells; then scan for a new single.Every candidate in column 2 lies in region E (row 3, column 2; row 4, column 2; row 5, column 2). Its cat must use that shared section. Exclude row 5, column 3 from the rest of region E.
Before step 2. Exclude 1 cells; then scan for a new single.The cat in column 2 must occupy one of row 3, column 2; row 4, column 2; row 5, column 2. Each of row 4, column 1; row 4, column 3 touches every candidate, so none can hold a cat.
Before step 3. Exclude 2 cells; then scan for a new single.column 3 has only one remaining candidate: row 3, column 3. Every other cell is excluded by earlier placements or deductions. Place the cat here.
Before step 4. Place one cat, then exclude 7 other cells.row 4 has only one remaining candidate: row 4, column 5. Every other cell is excluded by earlier placements or deductions. Place the cat here.
Before step 5. Place one cat, then exclude 4 other cells.row 2 has only one remaining candidate: row 2, column 1. Every other cell is excluded by earlier placements or deductions. Place the cat here.
Before step 6. Place one cat, then exclude 2 other cells.row 1 has only one remaining candidate: row 1, column 4. Every other cell is excluded by earlier placements or deductions. Place the cat here.
Before step 7. Place one cat, then exclude 0 other cells.row 5 has only one remaining candidate: row 5, column 2. Every other cell is excluded by earlier placements or deductions. Place the cat here.
Before step 8. Place one cat, then exclude 0 other cells.The final cats satisfy every row, column and region quota, with no edge or corner contact.
Cat positions: r1c4, r2c1, r3c3, r4c5, r5c2.
gm-5-0007 · 5×5 · practice
Practice single-candidate placements on another 5×5 board.
Read this walkthrough →gm-8-0053 · 8×8 · practice
Transfer single-candidate placements to a 8×8 grid; compare how the candidates change.
Read this walkthrough →gm-5-0012 · 5×5 · challenge
Compare this route with candidate locks, and check why that different rule is needed.
Read this walkthrough →
GridMew