7x7 Queens Puzzle #277

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 9-step reasoning is written out below.

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Step-by-step solution for puzzle #277

What follows is a complete solve of puzzle #277, worked the way a person works it rather than the way a computer does. It runs to 9 deductions — 7 queen placements and 2 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: last square in a region, region shadow, region confined to one line.

Show the full walkthrough (5 steps) — contains the solution

  1. Step 1. Only row 4, column 3 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 3, the rest of the mint region and every square adjacent to it — diagonals included.

  2. Step 2. 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.

  3. Step 3. The indigo region has 3 squares left, spread across rows 1 and 2, columns 2 and 4. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.

    Puzzle #277 after step 3: 2 of 7 queens placed
    The board after step 3 — 2 of 7 queens placed.

  4. Step 4. All of the slate region's remaining squares (2 open squares) lie in row 5. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.

  5. Step 5. 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: pale yellow has one square left, so its queen takes row 7, column 7; slate has one square left, so its queen takes row 5, column 6; amber has one square left, so its queen takes row 2, column 5; indigo has one square left, so its queen takes row 1, column 2; red has one square left, so its queen takes row 6, column 4. 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 4.

    Puzzle #277 after step 5: 7 of 7 queens placed
    The board after step 5 — 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 #277

Puzzle #277 is one of the medium-rated boards in the 7x7 set. Seven colors divide its 49 squares, and you win by placing seven queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.

Puzzle #277 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 #277 are: mint (1 square), blue (3 squares), pale yellow (3 squares), slate (4 squares), indigo (8 squares), amber (12 squares), red (18 squares). An even split would hand every color 7 squares, so the mint region is running 6 squares under that average while the red region is the roomiest area on the grid with 18 squares.

Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So mint, with 1 square, is under far more pressure than red with 18. A 17-square gap like this one rewards players who start where the choices are fewest.

Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #277, packing 100% of its 2×4 bounding box, whereas amber straggles across its 4×5 box at just 60%. 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 #277, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Mint covers 1 square, spanning 1 row and 1 column (rows 4–4, columns 3–3). It never leaves row 4, so its queen is locked to that row.

Blue occupies 3 squares within rows 3–4, columns 1–2.

Pale yellow: 3 squares across rows 6–7, columns 6–7.

Slate covers 4 squares, spanning 2 rows and 2 columns (rows 4–5, columns 6–7).

Indigo occupies 8 squares within rows 1–2, columns 1–4.

Amber: 12 squares across rows 1–4, columns 3–7.

Red covers 18 squares, spanning 4 rows and 6 columns (rows 4–7, columns 1–6).

Where to start on this board

Mint is the natural opening on #277: it is the smallest region on the grid at 1 square, boxed into rows 4–4 and columns 3–3. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.

Because mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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. Indigo, blue, slate and pale yellow 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 #277

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3, 5, 6 and 7 are the narrowest, touched by only 2 colors. Column 5 is the tightest column, with 2 colors.

The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 6 rows. Row 4, meeting 5 colors, is the opposite case — the busiest line on #277 and the last one you should expect to crack.

Working through the middle game

The middle of #277 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.

Two checks, run alternately, will carry you through the 49 squares of this grid. First: has any of the seven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 7x7 boards almost always run one of those checks and forget the other.

Resist the plausible-looking queen. On #277 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.

Why puzzle #277 is rated medium

The rating reflects how much the board concedes up front. Puzzle #277 has two 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 17 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a medium board from the rest.

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.

Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #277, start hunting for it near row 1.

Here is a shape check that gives nothing away: when #277 is solved, 3 queens sit on the outer edge of the grid and 4 sit inside it, with 1 queen in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.

How to play Queens

  1. The board is an N×N grid divided into N colored regions.
  2. Place exactly one queen (♛) in each row, each column, and each colored region.
  3. No two queens may touch each other — not horizontally, vertically, or diagonally.
  4. 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.
  5. 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 #277?

Puzzle #277 is rated medium. 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 #277 have only one solution?

Yes. Every puzzle in the 7x7 collection, including #277, 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 #277?

Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.