10x10 Queens Puzzle #279
Difficulty: hard. 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 18-step reasoning is written out below.
Previous puzzle · All 10x10 puzzles · Next puzzle
Step-by-step solution for puzzle #279
What follows is a complete solve of puzzle #279, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 10 queen placements and 8 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: region shadow, pairing argument on rows, region confined to one line, last square in a region, last square in a row, last square in a column.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Wherever mint ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. Here is the pairing argument. The indigo, amber, and blue regions have no open squares outside rows 1–3 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 9 squares come off in one stroke.
Step 3. The mint region has 3 squares left, spread across rows 4 and 5, columns 5 and 6. 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 4. Wherever slate 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.
The board after step 4 — 0 of 10 queens placed. Step 5. Mint cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 8 squares in all.
Step 6. Here is the pairing argument. The mint and slate regions have no open squares outside rows 4 and 5 — 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: 9 squares come off in one stroke.
Step 7. 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: red has one square left, so its queen takes row 6, column 4; mint has one square left, so its queen takes row 4, column 5; slate has one square left, so its queen takes row 5, column 7; row 3 is down to one square, putting a queen on row 3, column 1. 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 3, column 1.
Step 8. Sea green cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to sea green, so every square in it owned by another colour is dead: 4 squares in all.
The board after step 8 — 4 of 10 queens placed. Step 9. Column 3 now has exactly one open square, row 8, column 3, in the khaki region. Columns must each hold a queen, so that placement is forced. Everything else in row 8, in column 3, in khaki and in the ring around that square is now dead.
Step 10. Only row 10, column 2 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 2, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 11. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
Step 12. 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: column 10 is down to one square, putting a queen on row 9, column 10; column 9 is down to one square, putting a queen on row 2, column 9; indigo has one square left, so its queen takes row 1, column 6; pale yellow has one square left, so its queen takes row 7, column 8. 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 8.
The board after step 12 — 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 #279
10x10 puzzle #279 is rated hard. 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.
There is exactly one way to finish #279, 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 ten regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #279 are: mint (4 squares), amber (6 squares), blue (7 squares), indigo (8 squares), orange (8 squares), red (9 squares), sea green (11 squares), slate (12 squares), khaki (17 squares), pale yellow (18 squares). An even split would hand every color 10 squares, so the mint region is running 6 squares under that average while the pale yellow region is the roomiest area on the grid with 18 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Mint has only 4 places to put its queen; pale yellow has 18. The spread between them on this board is 14 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 #279, packing 78% of its 3×3 bounding box, whereas slate straggles across its 5×5 box at just 48%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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.
Mint: 4 squares across rows 3–5, columns 5–6.
Amber covers 6 squares, spanning 2 rows and 4 columns (rows 2–3, columns 6–9).
Blue occupies 7 squares within rows 1–3, columns 1–3.
Indigo: 8 squares across rows 1–3, columns 4–8.
Orange covers 8 squares, spanning 4 rows and 3 columns (rows 7–10, columns 8–10).
Red occupies 9 squares within rows 3–6, columns 1–4.
Sea green: 11 squares across rows 5–10, columns 1–3.
Slate covers 12 squares, spanning 5 rows and 5 columns (rows 1–5, columns 6–10).
Khaki occupies 17 squares within rows 6–10, columns 2–6.
Pale yellow: 18 squares across rows 5–10, columns 6–10.
Where to start on this board
Open on the tightest color. Here that is mint, confined to 4 squares between rows 3 and 5 and columns 5 and 6. Its queen has nowhere else to go, which means those 3 rows and 2 columns carry more constraint than anywhere else on #279.
Mint does not collapse onto a single line, so it will not hand you a queen on move one. What it does give you is a short list of 4 candidates. Take each one in turn, imagine the queen there, cross out its row, its column and the eight squares around it, and ask whether any other region is left with nowhere to go. One or two candidates usually fail that test immediately.
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 #279
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 4 are the narrowest, touched by only 3 colors. Columns 1, 4, 5 and 10 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 9 rows. Row 3 is the crowded extreme at 6 colors — worth revisiting later, not now.
Working through the middle game
The middle of #279 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.
The whole middle game reduces to two sweeps. Sweep the ten colors looking for one with a single square left; sweep the ten rows and ten columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 10x10 solve from a stalled one.
Resist the plausible-looking queen. On #279 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 #279 is rated hard
Ratings track how generous the opening is. On #279 you get no region pinned to a single row or column, a smallest color of 4 squares, a tightest row crossed by 3 colors, and a 14-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
Stuck on #279 despite the hard 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 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 #279 the place to look for one is around row 1.
A non-spoiling distribution check: solved, #279 carries 4 queens on the perimeter against 6 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 10x10 Queens puzzle #279?
Puzzle #279 is rated hard. Its smallest color region holds 4 squares, its tightest row is touched by 3 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 10x10 puzzle #279 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #279, 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 #279?
Start with the mint region — the most constrained color on this board, with 4 squares spanning rows 3–5 and columns 5–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.