How to solve Queens: regions, rows and the cells you can rule out
6 min read ·
Queens is the coloured-region puzzle that took off as a daily game on LinkedIn. One queen goes in every row, every column and every colour, and no two queens may touch, not even diagonally. On Puzzimo you can play as many as you like, at 7×7, 8×8 and 9×9.
Every Queens puzzle can be solved by logic alone. Most of the work is ruling cells out, and this guide shows the four ideas that do it fastest.
The rules
- Exactly one queen in every row and every column.
- Exactly one queen in every coloured region.
- Queens never touch, not even at a corner.
Start with the smallest regions
A region of two or three cells has very few places for its queen, so it's where the board opens up. Even before you know the exact cell, a small region rules out a lot: any cell that touches every cell of the region can't hold a queen, because whichever cell the region's queen takes, it would touch it.
Regions locked into a row or column
If every cell of a region lies in one row, that region's queen will be in that row, so the rest of the row can't hold a queen. Mark all of it. The same goes for a region that sits in one column.
It works the other way too: if, in some row, every remaining open cell belongs to one region, then that region's queen is in that row, and the region's cells in other rows can be marked.
Count regions against rows
This is the technique that cracks the hard boards. Look for a group of k regions that fit entirely inside k rows (or columns). Those k regions need k queens, and the k rows can hold only k queens, so every queen in those rows belongs to those regions. Every other cell in those rows can be marked.
For example, if two regions lie entirely within rows 3 and 4, then rows 3 and 4 are used up by those two regions: any cell of another colour in rows 3 or 4 is empty.
Mark every neighbour of a queen
Each queen you place rules out its whole row, its whole column, its whole region and the up to eight cells around it. Mark them straight away. A board full of 🐾 marks is much easier to read than a blank one, and it's often the marking that reveals the next queen: a row or region with a single unmarked cell left.
A solving routine
- Find the smallest regions and mark cells that touch all of their cells.
- Mark the rest of any row or column that contains a whole region.
- Look for k regions inside k rows or columns, and mark the other cells there.
- Place a queen wherever a row, column or region has one cell left, and mark its neighbours.
- Repeat; each queen usually leads straight to the next.
Practise
On Puzzimo, tap a cell to mark it 🐾 (tap again to clear), double-tap to place a queen, and drag to mark or clear many cells at once. A queen on a cell where the solution has none counts as a mistake: it's shown and turned into a mark, and the third mistake ends the round. Boards come in 7×7, 8×8 and 9×9, with a 7×7 daily challenge.
Frequently asked questions
What's the fastest way to solve a Queens puzzle?
Start from the smallest regions, mark the cells they rule out, and look for regions that sit entirely in one row or column. Those two steps usually place the first few queens within seconds.
Can I play more Queens puzzles after LinkedIn's daily one?
Yes. Puzzimo has unlimited Queens puzzles in three sizes, free and in the browser, plus a daily challenge with global leaderboards.
Do I ever need to guess in Queens?
No. Every Queens puzzle on Puzzimo has exactly one solution and can be reached by logic. If you're stuck, look for a group of regions that fits inside the same number of rows or columns.