8x8 Queens Puzzle #7
Difficulty: medium. Place 8 queens on this 8x8 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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #7
What follows is a complete solve of puzzle #7, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 8 queen placements and 9 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: region shadow, region confined to one line, last square in a region, line confined to one region, last square in a row.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Wherever amber ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 10 squares come off.
Step 3. Only row 5, column 2 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 2, in slate and in the ring around that square is now dead.
Step 4. 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. Row 3 and column 1 are now spoken for, along with the squares touching that queen.
The board after step 4 — 2 of 8 queens placed. Step 5. Indigo is down to 5 candidates in rows 1, 2, and 4, columns 3–5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
Step 6. The pale yellow region has 3 squares left, spread across rows 7 and 8, columns 3 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.
Step 7. Khaki cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 7 squares in all.
Step 8. All of the pale yellow region's remaining squares (2 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
Step 9. Indigo cannot leave column 4 — every one of its open squares (2 open squares) sits there. That column belongs to indigo, so every square in it owned by another colour is dead: 1 square in all.
The board after step 9 — 2 of 8 queens placed. Step 10. Every open square left in row 2 (2 open squares) belongs to the amber region. Since that row must contain a queen, amber is the colour that supplies it — so amber squares anywhere else on the board are out, 3 squares in all.
Step 11. Look along row 1: one square survives, row 1, column 4, which belongs to indigo. A row cannot be left empty, so the queen goes there. That clears row 1, column 4, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 12. Every open square left in row 4 (3 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 13. 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 6 is down to one square, putting a queen on row 6, column 6; amber has one square left, so its queen takes row 2, column 8; mint has one square left, so its queen takes row 4, column 7; khaki has one square left, so its queen takes row 8, column 5; pale yellow has one square left, so its queen takes row 7, 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 7, column 3.
The board after step 13 — 8 of 8 queens placed.
That completes the board: 8 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 8x8 Queens puzzle #7
8x8 puzzle #7 is rated medium. Eight colored regions cover its 64 squares, and your job is to seat eight queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Puzzle #7 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 #7 are: blue (2 squares), slate (3 squares), khaki (3 squares), amber (5 squares), red (7 squares), pale yellow (12 squares), indigo (13 squares), mint (19 squares). An even split would hand every color 8 squares, so the blue region is running 6 squares under that average while the mint region is the roomiest area on the grid with 19 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Blue is working with 2 squares while mint has 19 to spare, a gap of 17. 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 blue is the most solid, filling 100% of its 1×2 box, and indigo the most diffuse at 52% of its 5×5 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 #7, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Blue covers 2 squares, spanning 1 row and 2 columns (rows 3–3, columns 1–2). It never leaves row 3, so its queen is locked to that row.
Slate occupies 3 squares within rows 4–5, columns 1–2.
Khaki: 3 squares across rows 7–8, columns 4–5.
Amber covers 5 squares, spanning 2 rows and 3 columns (rows 1–2, columns 6–8).
Red occupies 7 squares within rows 5–8, columns 6–8.
Pale yellow: 12 squares across rows 5–8, columns 1–4.
Indigo covers 13 squares, spanning 5 rows and 5 columns (rows 1–5, columns 1–5).
Mint occupies 19 squares within rows 2–7, columns 4–8.
Where to start on this board
Begin where the choices are fewest. On this board that means blue, which owns just 2 squares inside a 1×2 window running from row 3 to row 3 and column 1 to column 2. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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, slate and khaki 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 #7
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Column 3 is the tightest column, with 2 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 7 rows. By contrast row 5 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
With eight queens to seat and eight regions competing over 64 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 8x8 boards quickly and players who stall halfway.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #7 is rated medium
The rating reflects how much the board concedes up front. Puzzle #7 has one region confined to a single row or column, its smallest color holds 2 squares, 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.
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 8x8
At 8x8 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 1 on this board.
As a sanity check rather than a spoiler: the finished solution to #7 puts 4 queens on the outer border and 4 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 8x8 Queens puzzle #7?
Puzzle #7 is rated medium. Its smallest color region holds 2 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 8x8 puzzle #7 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #7, has been verified to have exactly one valid arrangement of eight queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #7?
Start with the blue region — the most constrained color on this board, with 2 squares spanning rows 3–3 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.