7x7 Queens Puzzle #290
Difficulty: medium. Place 7 queens on this 7x7 board so that no two share a row, column or color region and none touch — including diagonally. This puzzle has exactly one solution, and it has been verified solvable by deduction alone: the complete 8-step reasoning is written out below.
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Step-by-step solution for puzzle #290
What follows is a complete solve of puzzle #290, worked the way a person works it rather than the way a computer does. It runs to 8 deductions — 7 queen placements and 1 elimination step that narrow the board between them. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the region confined to one line.
Techniques this board needs: last square in a region, region confined to one line, last square in a row.
Show the full walkthrough (4 steps) — contains the solution
Step 1. Only row 6, column 4 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 4, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. The pale yellow region is down to one open square, at row 7, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 2, the remaining pale yellow squares, and the ring of neighbours around row 7, column 2.
The board after step 2 — 2 of 7 queens placed. Step 3. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 7 squares in all.
Step 4. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: row 5 is down to one square, putting a queen on row 5, column 1; row 3 is down to one square, putting a queen on row 3, column 5; mint has one square left, so its queen takes row 4, column 7; indigo has one square left, so its queen takes row 1, column 6; amber has one square left, so its queen takes row 2, column 3. After each one, clear that row, that column, the rest of the colour and the ring of neighbours before looking for the next. The last of them seats the queen on row 2, column 3.
The board after step 4 — 7 of 7 queens placed.
That completes the board: 7 queens seated, one in every row, one in every column and one in every colour, with no two of them touching. Notice that nothing in the sequence above required a guess — each placement followed from an elimination already on the grid, which is what “single solution, solvable by logic” actually means in practice.
About 7x7 Queens puzzle #290
Board #290 of the 7x7 bank carries a medium rating. Its 49 squares are shared between seven colored regions, and the solution places seven queens: one per row, one per column, one per region, none of them side by side or corner to corner.
Like every board on this site, #290 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #290 are: red (1 square), mint (2 squares), pale yellow (3 squares), amber (4 squares), indigo (8 squares), blue (15 squares), slate (16 squares). An even split would hand every color 7 squares, so the red region is running 6 squares under that average while the slate region is the roomiest area on the grid with 16 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Red has only 1 place to put its queen; slate has 16. The spread between them on this board is 15 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Square count is only half the story — how a color is arranged counts too. Mint is the tidiest shape on #290, packing 100% of its 1×2 bounding box, whereas blue straggles across its 6×4 box at just 63%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Here is the full footprint of every color on puzzle #290, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Red occupies 1 square within rows 6–6, columns 4–4. It never leaves row 6, so its queen is locked to that row.
Mint: 2 squares across rows 4–4, columns 6–7. It never leaves row 4, so its queen is locked to that row.
Pale yellow covers 3 squares, spanning 1 row and 3 columns (rows 7–7, columns 2–4). It never leaves row 7, so its queen is locked to that row.
Amber occupies 4 squares within rows 1–2, columns 1–3.
Indigo: 8 squares across rows 1–3, columns 4–7.
Blue covers 15 squares, spanning 6 rows and 4 columns (rows 2–7, columns 4–7).
Slate occupies 16 squares within rows 2–7, columns 1–4.
Where to start on this board
Begin where the choices are fewest. On this board that means red, which owns just 1 square inside a 1×1 window running from row 6 to row 6 and column 4 to column 4. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. Then look at which colors just lost ground: on a grid this size that one observation usually forces a second region within a move or two.
Work outward to the other flat regions next. Mint, pale yellow and amber are no more than two rows tall, so their queens are confined to a narrow band. When two flat regions overlap the same pair of rows, those rows are spoken for and every other color is locked out of both — the single most productive pattern in the game, and it is live on this board.
The tightest lines on puzzle #290
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 5 are the narrowest, touched by only 2 colors. Columns 1 and 5 are the tightest columns, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 6 rows. Row 2 sits at the far end with 4 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
Keep alternating between two views of the board. In the region view you ask which of the seven colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 7x7 board unwinds.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #290 is rated medium
The rating reflects how much the board concedes up front. Puzzle #290 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 15 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
If #290 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
Techniques that work well at 7x7
At 7x7 the whole grid stays within a single glance, which makes systematic scanning practical. Read the rows in order and count the colors in each — a row touched by two colors is far more constrained than one touched by five, and that is usually where the next forced move hides. The board is small enough that re-scanning from the top after each placement costs almost nothing.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #290 the place to look for one is around row 1.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 3 queens in the middle, and nothing in the corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
How to play Queens
- The board is an N×N grid divided into N colored regions.
- Place exactly one queen (♛) in each row, each column, and each colored region.
- No two queens may touch each other — not horizontally, vertically, or diagonally.
- Tap once to mark a square with an X (where a queen can't go), tap again to place a queen, and once more to clear it.
- There is always exactly one valid solution. Use logic, never guessing, to find it.
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Questions about this puzzle
How hard is 7x7 Queens puzzle #290?
Puzzle #290 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #290 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #290, has been verified to have exactly one valid arrangement of seven queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #290?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.