The full logical solve of the hard Queens for September 15 to September 21, 2026, 10 × 10. 20 steps, 7 techniques, no guessing. Step through it, or jump to any step below.
The region at row 1, column 1 has one square left that can hold its queen, at row 1, column 1. Its queen goes there.
Every open square of the region at row 1, column 6 is in row 2. So row 2’s queen belongs to that region, and the rest of row 2 can’t have one.
The region at row 1, column 2 has one square left that can hold its queen, at row 3, column 4. Its queen goes there.
The region at row 2, column 1 has one square left that can hold its queen, at row 4, column 2. Its queen goes there.
The region at row 2, column 8 has one square left that can hold its queen, at row 5, column 10. Its queen goes there.
Every open square of the region at row 10, column 4 is in row 10. So row 10’s queen belongs to that region, and the rest of row 10 can’t have one.
Every open square of the region at row 5, column 2 is in column 3. So column 3’s queen belongs to that region, and the rest of column 3 can’t have one.
Every open square of column 8 is in the region at row 4, column 8. So that region’s queen is in column 8, and the region’s other squares can’t have one.
Column 9 has one square left that can hold its queen, at row 2, column 9. Its queen goes there.
Suppose a queen sat at row 6, column 6. It would rule out every open square of the region at row 3, column 5, which then has nowhere for its queen. So row 6, column 6 can’t have a queen.
Suppose a queen sat at row 7, column 7. It would rule out every open square of row 8, which then has nowhere for its queen. So row 7, column 7 can’t have a queen.
Suppose a queen sat at row 8, column 5. It would rule out every open square of the region at row 3, column 5, which then has nowhere for its queen. So row 8, column 5 can’t have a queen.
Suppose a queen sat at row 8, column 7. It would rule out every open square of row 9, which then has nowhere for its queen. So row 8, column 7 can’t have a queen.
Suppose a queen sat at row 9, column 6. It would rule out every open square of row 10, which then has nowhere for its queen. So row 9, column 6 can’t have a queen.
The open squares of the regions at row 5, column 2 and row 3, column 5 all sit inside rows 6 and 7. Those two rows hold exactly two queens, and the regions need all of them. So no other square in rows 6 and 7 can have a queen.
Column 7 has one square left that can hold its queen, at row 10, column 7. Its queen goes there.
The region at row 4, column 8 has one square left that can hold its queen, at row 8, column 8. Its queen goes there.
The region at row 5, column 6 has one square left that can hold its queen, at row 9, column 5. Its queen goes there.
The region at row 3, column 5 has one square left that can hold its queen, at row 7, column 6. Its queen goes there.
The region at row 5, column 2 has one square left that can hold its queen, at row 6, column 3. Its queen goes there.