GridMewA 6×6 puzzle from two locks to five placements
Solve original gm-6-0002 by reserving regions B and C, excluding shared neighbors and following column singles.
On this page
Begin with the one givenUse the candidate pair as a neighborhoodReturn to the group that started the chainApply the ideaCheck your understandingOriginal GridMew lesson · Updated 16 October 2026
Learning goal: Turn two row-to-region locks and a neighbor exclusion into a sequence of forced placements.
Begin with the one given
The fixed cat at r1c6 fills A. In row 2 the remaining candidates all lie in B, so B’s candidates in row 3 can be excluded. This first lock changes another row without placing a cat.
Row 3 is now restricted to the two leftmost C cells. Reserve C for row 3 and remove its candidates from the lower rows. The second lock comes from the first, so check the row-2 elimination before relying on it.
Use the candidate pair as a neighborhood
Both r3c1 and r3c2 touch r2c1 and r2c2. Those two upper cells can be excluded while both row-3 candidates remain open. Column 1 then has only r3c1 left.
Once that cat is placed, column 2 resolves at r6c2. Region D subsequently resolves at r4c3. This route alternates upper and lower deductions because complete columns connect parts of the board that do not touch.
Return to the group that started the chain
The first reservation never selected row 2’s cat. The later placements eventually force r2c4, and row 5 then completes at r5c5. A reservation can do useful work long before its own exact position is known.
Try this puzzle again with only the original given visible. Your checkpoint is the first new cat at r3c1: explain the two locks and the shared-neighbor exclusion that make it forced. There is no need to memorize the final six coordinates.
Apply the idea to gm-6-0002
r2c3 means row 2, column 3, counting from the top left.
The first lock reserves B for row 2; the second reserves C for row 3. Neither places a new cat. At the next checkpoint, r3c1 and r3c2 both touch r2c1 and r2c2, so the upper pair can be removed.
After those removals, column 1 resolves at r3c1. This is why the column single appears only after the exclusions. The later cats in rows 6 and 4 carry the constraints back into row 2, settling the group that started the chain.
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 occupies A. Row 2 is confined to B, and that reservation strips B’s candidates from row 3. Keep both row-3 possibilities until their shared effect has been used.
6×6 · 1 fixed cats · 8 explained deductions. Region sizes: A: 2 · B: 13 · C: 7 · D: 2 · E: 10 · F: 2.
A deduction worth checking
Row 3’s r3c1 and r3c2 are both in C. Reserving C for that row removes its lower cells; the next neighbor exclusion then forces column 1.
A move to double-check · r2c2
Both remaining row-3 candidates touch r2c2. The exclusion is valid before knowing which one will be chosen, so guessing between them would skip the useful deduction.
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.
B B B B B A B B B B B A C C B B B E C C D E E E C C D E E E C F F E E E
Fixed cats: row 1, column 6. One cat is required in each row, column and region.
Step-by-step walkthrough
1Use a candidate lock
Every candidate in row 2 lies in region B (row 2, column 1; row 2, column 2; row 2, column 3; row 2, column 4). Its cat must use that shared section. Exclude row 3, column 3; row 3, column 4; row 3, column 5 from the rest of region B.
Before step 1. Exclude 3 cells; then scan for a new single.2Use a candidate lock
Every candidate in row 3 lies in region C (row 3, column 1; row 3, column 2). Its cat must use that shared section. Exclude row 4, column 1; row 4, column 2; row 5, column 1; row 5, column 2; row 6, column 1 from the rest of region C.
Before step 2. Exclude 5 cells; then scan for a new single.3Exclude common neighbors
The cat in row 3 must occupy one of row 3, column 1; row 3, column 2. Each of row 2, column 1; row 2, column 2 touches every candidate, so none can hold a cat.
Before step 3. Exclude 2 cells; then scan for a new single.4Check column 1
column 1 has only one remaining candidate: row 3, column 1. Every other cell is excluded by earlier placements or deductions. Place the cat here.
Before step 4. Place one cat, then exclude 1 other cells.5Check column 2
column 2 has only one remaining candidate: row 6, column 2. 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.6Check region D
region D has only one remaining candidate: row 4, column 3. Every other cell is excluded by earlier placements or deductions. Place the cat here.
Before step 6. Place one cat, then exclude 4 other cells.7Check row 2
row 2 has only one remaining candidate: row 2, 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.8Check row 5
row 5 has only one remaining candidate: row 5, column 5. 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.Show solution · reveals all cat positions
The final cats satisfy every row, column and region quota, with no edge or corner contact.
Cat positions: r1c6, r2c4, r3c1, r4c3, r5c5, r6c2.
Try another puzzle
A row lock can force a cat in the same row
gm-6-0012 · 6×6 · challenge
Practice candidate locks on another 6×6 board.
Read this walkthrough →A column reservation unlocks a small top region
gm-5-0012 · 5×5 · challenge
Transfer candidate locks to a 5×5 grid; compare how the candidates change.
Read this walkthrough →Walk the narrow right-side regions before scanning rows
gm-8-0053 · 8×8 · practice
Compare this route with single-candidate placements, and check why that different rule is needed.
Read this walkthrough →Check your understanding
What turns column 1 from a choice into a single?
Show the explanation
The C reservation first removes its lower column-1 cells. The shared-neighbor step then removes r2c1. With the top row already occupied by its given, r3c1 is the surviving column-1 candidate.