How to solve queens puzzles: seven techniques with examples
A queens puzzle gives you a square grid cut into color regions and asks for one crown in every row, every column and every region, with no two crowns touching, not even at a corner. In Crowns, every board has exactly one solution and can be finished by reasoning alone, and seven techniques are enough for all of them. This guide explains each one, solves a full 5 by 5 board step by step, and ends with a routine for fresh grids.
The name comes from the eight queens puzzle, a chess problem first published in 1848, which asks for eight queens on a chessboard with no two sharing a row, a column or a diagonal. Crowns drops the long diagonals and adds regions, so two crowns may share a diagonal as long as they are not neighbours. Our history of the eight queens puzzle tells that story.
Marks do half the work
Every technique below works by ruling cells out. Tap a cell once to mark it with an X, your note that no crown can go there; tap twice for a crown and a third time to clear it. Drag across empty cells to mark many at once, or turn on Mark around new crowns and the game will mark a new crown's row, column, region and neighbours for you. A crown that breaks a rule turns red straight away, so a slip never hides.
The seven techniques
- A crown clears its neighbourhood. Once a crown is down, nothing else can go in its row, its column, its region or the eight cells around it. Mark them all before you look for the next step.
- The last cell standing. When a row, column or region has one open cell left, the crown goes there. Most crowns are found this way.
- A region inside one line. If every open cell of a region lies in the same row, that row's crown must belong to the region, so every other cell of the row is an X. Columns work the same way. A region shaped like a straight bar is the classic first move.
- A line inside one region. The reverse also holds. If every open cell of a row lies inside one region, the region's crown is in that row, and the rest of the region is empty. Look for this along the edges.
- The cell that would wipe out a region. Imagine a crown on a cell. If it would rule out every remaining cell of some region, row or column, it can't hold a crown. Small regions are the usual victims: when a region is down to two neighbouring cells, each cell running alongside the pair touches both of them, so every such cell is an X.
- Regions sharing lines. When two regions fit entirely inside the same two rows, those rows' two crowns must belong to them, so every other cell in the two rows is an X. Three regions inside three rows work the same way, and so do columns.
- A short what-if. On the hardest boards, try a crown in a likely cell and follow the simple steps for one or two more crowns. If that leaves a row, column or region with no open cell, the trial crown was impossible, so mark an X. Cells beside the smallest region make good trials, because a wrong crown there fails fast.
A worked 5 by 5 board
Rows are counted from the top and columns from the left. Five regions need five crowns.
- Region C is two cells in column 5, rows 1 and 2. Column 5's crown must be one of them, so mark the rest of column 5. That is technique 3.
- Region E is left with two open cells, columns 3 and 4 of row 5. Both are in row 5, so mark the rest of that row.
- Region D is now down to rows 3 and 4 of column 1. Mark the top two cells of column 1.
- Look at column 2. Its open cells, rows 1 to 4, all belong to region A, so A's crown is somewhere in column 2. Mark A's other open cells: row 3 column 3, and row 4 columns 3 and 4. That is technique 4.
- Row 1 column 4 and row 2 column 4 each touch both cells of region C, so a crown on either would wipe C out. Mark them. In the same way, row 3 column 2 and row 4 column 2 each touch both open cells of region D. Mark those too. That is technique 5.
- Row 4 now has a single open cell, column 1. Crown it and mark around it, which removes row 3 column 1. The right-hand board shows this moment.
- Row 3 has one open cell left, column 4, in region B. Crown it and mark around it, including row 2 column 5, which touches it at a corner.
- Region C is down to row 1 column 5: crown. That marks the rest of row 1 and leaves row 2 column 2 as region A's last cell: crown.
- Region E's last cell is row 5 column 3, since column 4 already has its crown. Crown it.
The finished board has crowns in row 1 column 5, row 2 column 2, row 3 column 4, row 4 column 1 and row 5 column 3. Notice the rhythm: every batch of marks made the next step visible. That chain reaction is normal, and it is why marking everything pays. The hardest step this board needs is the wipe-out in step 5, so Crowns would label it Medium.
How to scan a fresh board
A fresh board looks blank, but it almost always offers a first step. Work down this list and act on the first thing you find:
- Bars. Any region that sits in a single row or column clears the rest of that line.
- Edges. Check the outer rows and columns for a line whose open cells all belong to one region.
- Tiny regions. For each region of two or three cells, mark every cell that touches all of them.
- Pairs. Look for two regions living inside the same two rows or columns, then for three in three.
- Repeat. After every batch of marks, look again at the rows, columns and regions you just touched.
- Only then, a what-if, starting beside the smallest region.
Boards grow from 5 by 5 in the first ten levels to 10 by 10 from level 321. The daily puzzle is 7 by 7 on Monday and Tuesday, 8 by 8 from Wednesday to Friday and 9 by 9 at the weekend, so the routine gets a real workout by Sunday.
Hints and difficulty labels
Each puzzle comes with three free hints. A hint explains its step in one sentence and names the regions by color, so treat it as a short lesson: read the sentence, find the technique above, and apply it yourself.
The labels Gentle, Easy, Medium, Hard and Fiendish track the hardest step a board needs. Gentle boards fall to the first three techniques and Easy boards add the fourth, a line inside one region. Medium boards need a wipe-out, Hard boards need regions sharing lines, and Fiendish boards are the ones that call for a what-if. If you enjoy this kind of elimination, the same habits carry straight over to binary puzzles.