7x7 Queens Puzzle #263
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 14-step reasoning is written out below.
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Step-by-step solution for puzzle #263
What follows is a complete solve of puzzle #263, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 7 queen placements and 7 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 line confined to one region.
Techniques this board needs: last square in a region, region shadow, region confined to one line, line confined to one region, last square in a row.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 7, column 7 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 7, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 2. Slate is down to 4 candidates in rows 3 and 5, columns 4–6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
Step 3. Red cannot leave row 6 — every one of its open squares (2 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 5 squares in all.
Step 4. All of the slate region's remaining squares (2 open squares) lie in column 6. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
The board after step 4 — 1 of 7 queens placed. Step 5. Amber cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 4 squares in all.
Step 6. The red region is down to one open square, at row 6, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 4, the remaining red squares, and the ring of neighbours around row 6, column 4.
Step 7. Blue cannot leave column 3 — every one of its open squares (3 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 2 squares in all.
The board after step 7 — 2 of 7 queens placed. Step 8. Every open square left in row 4 (2 open squares) belongs to the mint region. Since that row must contain a queen, mint is the colour that supplies it — so mint squares anywhere else on the board are out, 3 squares in all.
Step 9. Look along row 5: one square survives, row 5, column 6, which belongs to slate. A row cannot be left empty, so the queen goes there. Everything else in row 5, in column 6, in slate and in the ring around that square is now dead.
Step 10. All of the mint region's remaining squares (2 open squares) lie in row 4. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: row 3 is down to one square, putting a queen on row 3, column 3; mint has one square left, so its queen takes row 4, column 1; indigo has one square left, so its queen takes row 1, column 2; amber has one square left, so its queen takes row 2, column 5. 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 5.
The board after step 11 — 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 #263
7x7 puzzle #263 is rated hard. Seven colored regions cover its 49 squares, and your job is to seat seven queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Puzzle #263 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 #263 are: pale yellow (1 square), indigo (5 squares), red (5 squares), amber (6 squares), slate (8 squares), blue (10 squares), mint (14 squares). An even split would hand every color 7 squares, so the pale yellow region is running 6 squares under that average while the mint region is the roomiest area on the grid with 14 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Pale yellow is working with 1 square while mint has 14 to spare, a gap of 13. Attack the cramped end and the roomy regions tend to resolve themselves.
A region's outline can constrain it more than its size does. Here amber is the most solid, filling 100% of its 2×3 box, and slate the most diffuse at 50% of its 4×4 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #263 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Pale yellow occupies 1 square within rows 7–7, columns 7–7. It never leaves row 7, so its queen is locked to that row.
Indigo: 5 squares across rows 1–3, columns 1–2.
Red covers 5 squares, spanning 2 rows and 3 columns (rows 6–7, columns 4–6).
Amber occupies 6 squares within rows 1–2, columns 5–7.
Slate: 8 squares across rows 3–6, columns 4–7.
Blue covers 10 squares, spanning 4 rows and 4 columns (rows 1–4, columns 3–6).
Mint occupies 14 squares within rows 3–7, columns 1–4.
Where to start on this board
The most constrained color is where a solve should begin, and on #263 that is pale yellow with 1 square. It reaches from row 7 to row 7 and from column 7 to column 7 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Because pale yellow never leaves row 7, its queen must be in that row — and that instantly settles row 7 for everyone else. Sweep along it and X out every square that is not pale yellow. 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. Amber and red 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 #263
A quick way to find the next move is to count how many different colors touch each line. On this board, row 5 is the narrowest, touched by only 2 colors. Columns 1, 2 and 3 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 3 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.
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 #263 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 13. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 5 on this board.
A non-spoiling distribution check: solved, #263 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 #263?
Puzzle #263 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #263 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #263, 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 #263?
Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.