8x8 Queens Puzzle #249
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 11-step reasoning is written out below.
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Step-by-step solution for puzzle #249
What follows is a complete solve of puzzle #249, worked the way a person works it rather than the way a computer does. It runs to 11 deductions — 8 queen placements and 3 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 pairing argument on rows.
Techniques this board needs: last square in a region, region confined to one line, pairing argument on rows.
Show the full walkthrough (5 steps) — contains the solution
Step 1. Only row 3, column 8 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 8, the rest of the blue region and every square adjacent to it — diagonals included.
Step 2. All of the khaki region's remaining squares (2 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 7 squares come off.
Step 3. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 5 squares in all.
The board after step 3 — 1 of 8 queens placed. Step 4. Here is the pairing argument. The indigo and amber regions have no open squares outside rows 1 and 2 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 3 squares come off in one stroke.
Step 5. 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: mint has one square left, so its queen takes row 4, column 3; pale yellow has one square left, so its queen takes row 7, column 2; indigo has one square left, so its queen takes row 1, column 4; amber has one square left, so its queen takes row 2, column 6; khaki has one square left, so its queen takes row 8, column 5; slate has one square left, so its queen takes row 5, column 1; 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.
The board after step 5 — 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 #249
Puzzle #249 is one of the medium-rated boards in the 8x8 set. Eight colors divide its 64 squares, and you win by placing eight queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
There is exactly one way to finish #249, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these eight regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #249 are: blue (1 square), khaki (2 squares), indigo (4 squares), pale yellow (6 squares), mint (7 squares), amber (12 squares), slate (13 squares), red (19 squares). An even split would hand every color 8 squares, so the blue region is running 7 squares under that average while the red region is the roomiest area on the grid with 19 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 blue, with 1 square, is under far more pressure than red with 19. A 18-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. Blue is the tidiest shape on #249, packing 100% of its 1×1 bounding box, whereas slate straggles across its 4×6 box at just 54%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #249 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.
Blue: 1 square across rows 3–3, columns 8–8. It never leaves row 3, so its queen is locked to that row.
Khaki covers 2 squares, spanning 1 row and 2 columns (rows 8–8, columns 4–5). It never leaves row 8, so its queen is locked to that row.
Indigo occupies 4 squares within rows 1–2, columns 2–4.
Pale yellow: 6 squares across rows 7–8, columns 1–4.
Mint covers 7 squares, spanning 4 rows and 3 columns (rows 1–4, columns 1–3).
Amber occupies 12 squares within rows 1–3, columns 4–8.
Slate: 13 squares across rows 4–7, columns 1–6.
Red covers 19 squares, spanning 6 rows and 5 columns (rows 3–8, columns 4–8).
Where to start on this board
Open on the tightest color. Here that is blue, confined to 1 square between rows 3 and 3 and columns 8 and 8. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #249.
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. Khaki, indigo 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 #249
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5 and 6 are the narrowest, touched by only 2 colors. Column 7 is the tightest column, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 7 rows. Row 3 sits at the far end with 4 colors crossing it; it will almost certainly be among the last to settle.
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.
The whole middle game reduces to two sweeps. Sweep the eight colors looking for one with a single square left; sweep the eight rows and eight columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 8x8 solve from a stalled one.
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 #249 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 18. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
Stuck on #249 despite the medium rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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.
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 #249, start hunting for it near row 5.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 4 queens in the middle, and nothing in the corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #249?
Puzzle #249 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 8x8 puzzle #249 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #249, 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 #249?
Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.