8x8 Queens Puzzle #15
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 13-step reasoning is written out below.
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Step-by-step solution for puzzle #15
What follows is a complete solve of puzzle #15, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 8 queen placements and 5 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 confined to one line, region shadow, last square in a region.
Show the full walkthrough (7 steps) — contains the solution
Step 1. Amber cannot leave column 8 — 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: 8 squares in all.
Step 2. Blue is down to 5 candidates in rows 3–5, columns 4–6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 3. Only row 5, column 7 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 7, in slate and in the ring around that square is now dead.
Step 4. Wherever blue 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.
The board after step 4 — 1 of 8 queens placed. Step 5. Mint is down to 5 candidates in rows 3 and 4, columns 1–3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 6. The red region has 3 squares left, spread across rows 6 and 7, columns 1 and 2. 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. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: pale yellow has one square left, so its queen takes row 7, column 3; red has one square left, so its queen takes row 6, column 1; mint has one square left, so its queen takes row 4, column 2; blue has one square left, so its queen takes row 3, column 6; amber has one square left, so its queen takes row 2, column 8; khaki has one square left, so its queen takes row 8, column 5; indigo has one square left, so its queen takes row 1, 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 1, column 4.
The board after step 7 — 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 #15
8x8 puzzle #15 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 #15 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 #15 are: amber (2 squares), pale yellow (2 squares), slate (3 squares), red (5 squares), blue (6 squares), mint (8 squares), indigo (16 squares), khaki (22 squares). An even split would hand every color 8 squares, so the amber region is running 6 squares under that average while the khaki region is the roomiest area on the grid with 22 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Amber has only 2 places to put its queen; khaki has 22. The spread between them on this board is 20 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
A region's outline can constrain it more than its size does. Here amber is the most solid, filling 100% of its 2×1 box, and blue the most diffuse at 50% of its 3×4 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Amber: 2 squares across rows 2–3, columns 8–8. It sits wholly inside column 8, so its queen must be in that column.
Pale yellow covers 2 squares, spanning 1 row and 2 columns (rows 7–7, columns 2–3). It never leaves row 7, so its queen is locked to that row.
Slate occupies 3 squares within rows 4–5, columns 7–8.
Red: 5 squares across rows 5–7, columns 1–2.
Blue covers 6 squares, spanning 3 rows and 4 columns (rows 3–5, columns 4–7).
Mint occupies 8 squares within rows 3–5, columns 1–5.
Indigo: 16 squares across rows 1–3, columns 1–8.
Khaki covers 22 squares, spanning 4 rows and 8 columns (rows 5–8, columns 1–8).
Where to start on this board
Begin where the choices are fewest. On this board that means amber, which owns just 2 squares inside a 2×1 window running from row 2 to row 3 and column 8 to column 8. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because amber stays inside column 8, its queen belongs to that column and no other region may use it. Cross out the rest of column 8 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
Work outward to the other flat regions next. Pale yellow and slate 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 #15
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 8 are the narrowest, touched by only 1 color. Column 6 is the tightest column, with 3 colors.
A line with few colors is a line close to resolving. Where only 1 color appear, one of them owns the row outright and the others must fit into the remaining 7 rows. Row 5 is the crowded extreme at 5 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.
Two checks, run alternately, will carry you through the 64 squares of this grid. First: has any of the eight regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 8x8 boards almost always run one of those checks and forget the other.
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 #15 is rated medium
Ratings track how generous the opening is. On #15 you get two regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 1 color, and a 20-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.
Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.
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.
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 #15 the place to look for one is around row 1.
A non-spoiling distribution check: solved, #15 carries 4 queens on the perimeter against 4 queens inside, with the corners empty. 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 8x8 Queens puzzle #15?
Puzzle #15 is rated medium. Its smallest color region holds 2 squares, its tightest row is touched by 1 color, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 8x8 puzzle #15 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #15, 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 #15?
Start with the amber region — the most constrained color on this board, with 2 squares spanning rows 2–3 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.