7x7 Queens Puzzle #256

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 9-step reasoning is written out below.

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Step-by-step solution for puzzle #256

What follows is a complete solve of puzzle #256, 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 (6 steps) — contains the solution

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

  2. Step 2. The amber region is down to one open square, at row 2, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 6, the remaining amber squares, and the ring of neighbours around row 2, column 6.

  3. Step 3. Only row 4, column 5 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 5, in mint and in the ring around that square is now dead.

    Puzzle #256 after step 3: 3 of 7 queens placed
    The board after step 3 — 3 of 7 queens placed.

  4. Step 4. Wherever blue ends up among its 2 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.

  5. Step 5. Pale yellow cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 4 squares in all.

  6. Step 6. 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: blue has one square left, so its queen takes row 3, column 3; slate has one square left, so its queen takes row 5, column 1; pale yellow has one square left, so its queen takes row 7, column 2; red has one square left, so its queen takes row 6, column 7. 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 7.

    Puzzle #256 after step 6: 7 of 7 queens placed
    The board after step 6 — 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 #256

This is puzzle number 256 in the 7x7 collection, rated hard. The grid holds 49 squares split between seven colored regions, and a finished board carries seven queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.

Puzzle #256 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 #256 are: indigo (1 square), amber (5 squares), pale yellow (5 squares), blue (6 squares), mint (9 squares), slate (10 squares), red (13 squares). An even split would hand every color 7 squares, so the indigo region is running 6 squares under that average while the red region is the roomiest area on the grid with 13 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 indigo, with 1 square, is under far more pressure than red with 13. A 12-square gap like this one rewards players who start where the choices are fewest.

A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and pale yellow the most diffuse at 56% of its 3×3 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

Here is the full footprint of every color on puzzle #256, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

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

Amber occupies 5 squares within rows 1–2, columns 5–7.

Pale yellow: 5 squares across rows 5–7, columns 2–4.

Blue covers 6 squares, spanning 5 rows and 2 columns (rows 1–5, columns 2–3).

Mint occupies 9 squares within rows 2–4, columns 4–7.

Slate: 10 squares across rows 1–7, columns 1–2.

Red covers 13 squares, spanning 4 rows and 5 columns (rows 4–7, columns 3–7).

Where to start on this board

Open on the tightest color. Here that is indigo, confined to 1 square between rows 1 and 1 and columns 4 and 4. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #256.

Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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 is no more than two rows tall, so its queen is 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 #256

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

The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 6 rows. Row 5, meeting 4 colors, is the opposite case — the busiest line on #256 and the last one you should expect to crack.

Working through the middle game

After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.

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.

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 #256 is rated hard

The rating reflects how much the board concedes up front. Puzzle #256 has two regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 12 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

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.

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 #256, start hunting for it near column 1.

Here is a shape check that gives nothing away: when #256 is solved, 4 queens sit on the outer edge of the grid and 3 sit inside it, and no queen lands 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 #256?

Puzzle #256 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.

Does 7x7 puzzle #256 have only one solution?

Yes. Every puzzle in the 7x7 collection, including #256, 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 #256?

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