10x10 Queens Puzzle #247
Difficulty: easy. Place 10 queens on this 10x10 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 #247
What follows is a complete solve of puzzle #247, worked the way a person works it rather than the way a computer does. It runs to 11 deductions — 10 queen placements and 1 elimination step 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 confined to one line.
Techniques this board needs: last square in a region, region confined to one line, last square in a row.
Show the full walkthrough (3 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: blue has one square left, so its queen takes row 3, column 10; amber has one square left, so its queen takes row 2, column 8; indigo has one square left, so its queen takes row 1, column 6; sea green has one square left, so its queen takes row 10, column 2; khaki has one square left, so its queen takes row 8, column 1; slate has one square left, so its queen takes row 5, 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 5, column 3.
Step 2. Red cannot leave column 9 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 1 square in all.
The board after step 2 — 6 of 10 queens placed. Step 3. 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: orange has one square left, so its queen takes row 9, column 7; row 4 is down to one square, putting a queen on row 4, column 5; pale yellow has one square left, so its queen takes row 7, column 4; red has one square left, so its queen takes row 6, column 9. 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 9.
The board after step 3 — 10 of 10 queens placed.
That completes the board: 10 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 10x10 Queens puzzle #247
10x10 puzzle #247 is rated easy. Ten colored regions cover its 100 squares, and your job is to seat ten queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Like every board on this site, #247 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #247 are: blue (1 square), sea green (1 square), amber (4 squares), khaki (5 squares), slate (7 squares), indigo (9 squares), orange (12 squares), pale yellow (17 squares), red (19 squares), mint (25 squares). An even split would hand every color 10 squares, so the blue region is running 9 squares under that average while the mint region is the roomiest area on the grid with 25 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Blue has only 1 place to put its queen; mint has 25. The spread between them on this board is 24 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Square count is only half the story — how a color is arranged counts too. Blue is the tidiest shape on #247, packing 100% of its 1×1 bounding box, whereas indigo straggles across its 3×6 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #247 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 covers 1 square, spanning 1 row and 1 column (rows 3–3, columns 10–10). It never leaves row 3, so its queen is locked to that row.
Sea green occupies 1 square within rows 10–10, columns 2–2. It never leaves row 10, so its queen is locked to that row.
Amber: 4 squares across rows 1–2, columns 8–10.
Khaki covers 5 squares, spanning 3 rows and 2 columns (rows 8–10, columns 1–2).
Slate occupies 7 squares within rows 4–6, columns 1–3.
Indigo: 9 squares across rows 1–3, columns 4–9.
Orange covers 12 squares, spanning 4 rows and 5 columns (rows 7–10, columns 6–10).
Pale yellow occupies 17 squares within rows 5–10, columns 1–5.
Red: 19 squares across rows 3–9, columns 7–10.
Mint covers 25 squares, spanning 7 rows and 7 columns (rows 1–7, columns 1–7).
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 10 and 10. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #247.
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. Sea green and amber 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 #247
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2 and 4 are the narrowest, touched by only 3 colors. Columns 3, 4, 5 and 6 are the tightest columns, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 9 rows. Row 10 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
The middle of #247 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.
With ten queens to seat and ten regions competing over 100 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 10x10 boards quickly and players who stall halfway.
Resist the plausible-looking queen. On #247 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 #247 is rated easy
What earns a board its rating is the shape of its opening. Here that opening offers four single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 24. 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.
If #247 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
Techniques that work well at 10x10
At 10x10 a full re-scan after every move starts to get slow, so work locally instead. Once a queen goes down, check only the regions, rows and columns that placement actually touched — that is where new information appeared. Fall back to a complete sweep only when the local pass turns up nothing, and your solve times will drop noticeably.
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 #247 the place to look for one is around row 1.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 6 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 10x10 Queens puzzle #247?
Puzzle #247 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #247 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #247, has been verified to have exactly one valid arrangement of ten queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #247?
Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 10–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.