7x7 Queens Puzzle #270
Difficulty: hard. 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 13-step reasoning is written out below.
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Step-by-step solution for puzzle #270
What follows is a complete solve of puzzle #270, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 7 queen placements and 6 elimination steps 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 shadow.
Techniques this board needs: region shadow, region confined to one line, last square in a region.
Show the full walkthrough (8 steps) — contains the solution
Step 1. Wherever indigo ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 2. All of the blue region's remaining squares (3 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
Step 3. The slate region has 5 squares left, spread across rows 2–5, columns 6 and 7. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 4. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
The board after step 4 — 0 of 7 queens placed. Step 5. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 4 squares in all.
Step 6. The blue region is down to one open square, at row 3, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 1, the remaining blue squares, and the ring of neighbours around row 3, column 1.
Step 7. Mint cannot leave row 4 — every one of its open squares (3 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 2 squares in all.
Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: slate has one square left, so its queen takes row 5, column 6; indigo has one square left, so its queen takes row 1, column 5; amber has one square left, so its queen takes row 2, column 3; mint has one square left, so its queen takes row 4, column 4; pale yellow has one square left, so its queen takes row 7, column 7; red has one square left, so its queen takes row 6, column 2. 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 6, column 2.
The board after step 8 — 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 #270
Board #270 of the 7x7 bank carries a hard 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.
Puzzle #270 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #270 are: indigo (3 squares), blue (3 squares), slate (6 squares), amber (7 squares), mint (7 squares), red (10 squares), pale yellow (13 squares). An even split would hand every color 7 squares, so the indigo region is running 4 squares under that average while the pale yellow region is the roomiest area on the grid with 13 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 3 places to put its queen; pale yellow has 13. The spread between them on this board is 10 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Look at arrangement as well as area. Blue is the densest region on this grid at 100% of a 3×1 frame; slate is the loosest, occupying only 60% of its 5×2 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a hard board.
Indigo: 3 squares across rows 1–2, columns 5–6.
Blue covers 3 squares, spanning 3 rows and 1 column (rows 1–3, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Slate occupies 6 squares within rows 1–5, columns 6–7.
Amber: 7 squares across rows 1–2, columns 2–5.
Mint covers 7 squares, spanning 2 rows and 4 columns (rows 3–4, columns 2–5).
Red occupies 10 squares within rows 4–7, columns 1–3.
Pale yellow: 13 squares across rows 4–7, columns 3–7.
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 3 squares inside a 2×2 window running from row 1 to row 2 and column 5 to column 6. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
With 2 rows and 2 columns of room, indigo needs narrowing rather than solving outright. Test its 3 squares against the neighbours: a candidate that would strand another color is dead, and eliminating even two of them tightens the whole corner of the board around rows 1–2.
Work outward to the other flat regions next. Amber and mint 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 #270
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 6 and 7 are the narrowest, touched by only 2 colors. Columns 1 and 7 are the tightest columns, with 2 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 6 rows. Row 4 is the crowded extreme at 4 colors — worth revisiting later, not now.
Working through the middle game
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
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.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #270 is rated hard
The hard label comes out of four measurable things about #270: one of its regions is locked to one row or column, its smallest color spans 3 squares, its least crowded row meets 2 colors, and its largest and smallest regions differ by 10. Boards that score tight on those measures give up their first queen fast.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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 #270 the place to look for one is around row 6.
A non-spoiling distribution check: solved, #270 carries 3 queens on the perimeter against 4 queens inside, 1 of them cornered. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.
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 #270?
Puzzle #270 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #270 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #270, 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 #270?
Start with the indigo region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 5–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.