A corner singleton starts an upper-to-lower staircase

Original puzzle gm-8-0054

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

8 × 8 practice

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

Puzzle board · starting state

gm-8-0054: 8×8 regional boardEEBBDCCAEEEBDCCCEEEDDDCCEEEDDDDDEEEEFFDDEHEGFFFFHHGGFFFFHHGGFFFF

How to approach this board

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

A is only r1c8. Together with the r7c3 given, it reduces B to r2c4, then C to r3c7. Repeated regional singles carry the solve downward without requiring a candidate lock.

8×8 · 1 fixed cats · 7 explained deductions. Region sizes: A: 1 · B: 3 · C: 7 · D: 12 · E: 17 · F: 14 · G: 5 · H: 5.

A deduction worth checking

D next forces r4c5. Its neighborhood removes r5c6, helping the column-2 single appear in row 5.

gm-8-0054: 8×8 regional boardE×E×B×B×D×C×C×AE×E×E×BD×C×C×C×E×E×E×D×D×D×CC×EEE×D×DD×D×D×EEE×E×FFD×D×EH×E×G×FFF×F×H×H×GG×F×F×F×F×HH×G×G×FFF×F×
Position before step 4. Review the technique.
A move to double-check · r5c6

r5c6 cannot be retained after r4c5. Their immediate corner contact applies even though the cells sit in different regions.

gm-8-0054: 8×8 regional boardE×E×B×B×D×C×C×AE×E×E×BD×C×C×C×E×E×E×D×D×D×CC×EEE×D×DD×D×D×EEE×E×FFD×D×EH×E×G×FFF×F×H×H×GG×F×F×F×F×HH×G×G×FFF×F×

Green marks the cell being discussed, not a cat to place. This is the position before step 4; 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.

E E B B D C C A
E E E B D C C C
E E E D D D C C
E E E D D D D D
E E E E F F D D
E H E G F F F F
H H G G F F F F
H H G G F F F F

Fixed cats: row 7, column 3. One cat is required in each row, column and region.

Step-by-step walkthrough

1Check region A

region A has only one remaining candidate: row 1, column 8. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-8-0054: 8×8 regional boardEEB×BDCCAEEE×BDCCCEEE×DDDCCEEE×DDDDDEEE×EFFDDEH×E×G×FFFFH×H×GG×F×F×F×F×HH×G×G×FFFFBefore step 1. Place one cat, then exclude 13 other cells.

2Check region B

region B has only one remaining candidate: row 2, column 4. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-8-0054: 8×8 regional boardE×E×B×B×D×C×C×AEEE×BDCC×C×EEE×DDDCC×EEE×DDDDD×EEE×EFFDD×EH×E×G×FFFF×H×H×GG×F×F×F×F×HH×G×G×FFFF×Before step 2. Place one cat, then exclude 8 other cells.

3Check region C

region C has only one remaining candidate: row 3, column 7. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-8-0054: 8×8 regional boardE×E×B×B×D×C×C×AE×E×E×BD×C×C×C×EEE×D×D×DCC×EEE×D×DDDD×EEE×E×FFDD×EH×E×G×FFFF×H×H×GG×F×F×F×F×HH×G×G×FFFF×Before step 3. Place one cat, then exclude 8 other cells.

4Check region D

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

gm-8-0054: 8×8 regional boardE×E×B×B×D×C×C×AE×E×E×BD×C×C×C×E×E×E×D×D×D×CC×EEE×D×DD×D×D×EEE×E×FFD×D×EH×E×G×FFF×F×H×H×GG×F×F×F×F×HH×G×G×FFF×F×Before step 4. Place one cat, then exclude 6 other cells.

5Check column 2

column 2 has only one remaining candidate: row 5, column 2. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-8-0054: 8×8 regional boardE×E×B×B×D×C×C×AE×E×E×BD×C×C×C×E×E×E×D×D×D×CC×E×E×E×D×DD×D×D×EEE×E×F×F×D×D×EH×E×G×F×FF×F×H×H×GG×F×F×F×F×HH×G×G×F×FF×F×Before step 5. Place one cat, then exclude 2 other cells.

6Check row 6

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

gm-8-0054: 8×8 regional boardE×E×B×B×D×C×C×AE×E×E×BD×C×C×C×E×E×E×D×D×D×CC×E×E×E×D×DD×D×D×E×EE×E×F×F×D×D×E×H×E×G×F×FF×F×H×H×GG×F×F×F×F×HH×G×G×F×FF×F×Before step 6. Place one cat, then exclude 1 other cells.

7Check row 8

row 8 has only one remaining candidate: row 8, column 1. Every other cell is excluded by earlier placements or deductions. Place the cat here.

gm-8-0054: 8×8 regional boardE×E×B×B×D×C×C×AE×E×E×BD×C×C×C×E×E×E×D×D×D×CC×E×E×E×D×DD×D×D×E×EE×E×F×F×D×D×E×H×E×G×F×FF×F×H×H×GG×F×F×F×F×HH×G×G×F×F×F×F×Before 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-8-0054: 8×8 regional boardEEBBDCCAEEEBDCCCEEEDDDCCEEEDDDDDEEEEFFDDEHEGFFFFHHGGFFFFHHGGFFFF

Cat positions: r1c8, r2c4, r3c7, r4c5, r5c2, r6c6, r7c3, r8c1.

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How this puzzle and its reasoning are verified