GridMewA 5×5 puzzle solved through candidate exclusions
Follow gm-5-0003 through shared neighbors, a bottom-region lock and the first forced cat.
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Why this small board needs patienceUse the bottom region without choosing its cellFind the first cat, then update every groupApply the ideaCheck your understandingOriginal GridMew lesson · Updated 16 October 2026
Learning goal: Complete a compact board whose early deductions remove candidates rather than place cats.
Why this small board needs patience
gm-5-0003 starts with one fixed cat at r1c5. The first new cat does not arrive until the eighth deduction. If you search only for immediate placements, the position can look stalled even while useful information is available.
Start with the remaining candidates of row 2 and column 4. Their shared neighborhoods remove r3c2 and r4c3 respectively. These are local contact arguments, not decisions about where either group’s cat will go.
Use the bottom region without choosing its cell
E is restricted to r5c3 and r5c4 after the given is accounted for. Reserving row 5 for E excludes the two D cells at its left end. The remaining bottom-row pair then excludes r4c4 through its common neighborhood.
Later, the surviving candidates of column 2 are separated vertically. The same common-neighbor principle still applies. The complete sequence below preserves these intermediate positions so that the exclusions can be checked before the answer is shown.
Find the first cat, then update every group
The exclusions eventually leave row 3 with r3c4. Placing that cat removes r5c4 through column 4 and lets row 5 resolve at r5c3. From here the remaining rows finish by singles.
After completing this route, try explaining the E-to-row-5 lock in one sentence without naming the final E cat. If the explanation needs the answer diagram, return to the candidate pair and use the row and region quotas instead.
Apply the idea to gm-5-0003
r2c3 means row 2, column 3, counting from the top left.
Use the E-to-row-5 reservation as a checkpoint. At this point E still has two possible cat cells. Its value is that it removes r5c1 and r5c2 outside E, after which the bottom row’s shared neighborhood can be used.
Later, column 2 has separated candidates at r2c2 and r4c2. Their shared neighbor r3c3 is still excluded: candidate cells need not touch each other for this rule to apply. Compare that situation with the earlier neighboring pair in row 5.
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
1Exclude 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.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.
Try another puzzle
A column reservation unlocks a small top region
gm-5-0012 · 5×5 · challenge
Practice candidate locks on another 5×5 board.
Read this walkthrough →Two row reservations prepare a column single
gm-6-0002 · 6×6 · challenge
Transfer candidate locks to a 6×6 grid; compare how the candidates change.
Read this walkthrough →A full column reservation starts four linked locks
gm-8-0005 · 8×8 · challenge
Compare this route with shared-neighbor exclusions, and check why that different rule is needed.
Read this walkthrough →Check your understanding
Does the reservation of row 5 tell you immediately whether E uses r5c3 or r5c4?
Show the explanation
No. It only locates E’s cat within that pair. Choosing one now would turn a valid exclusion chain into a guess.