10x10 Queens Puzzle #278
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #278
What follows is a complete solve of puzzle #278, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 10 queen placements and 6 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 shadow, region confined to one line, pairing argument on rows, last square in a column.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 5, column 7 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 7, the rest of the slate region and every square adjacent to it — diagonals included.
Step 2. Indigo is down to 5 candidates in rows 1 and 2, columns 6, 8, 9, and 10, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
Step 3. Only row 2, column 10 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 10, in amber and in the ring around that square is now dead.
Step 4. The indigo region is down to one open square, at row 1, column 8. Every colour holds exactly one queen, so that square is forced. Row 1 and column 8 are now spoken for, along with the squares touching that queen.
The board after step 4 — 3 of 10 queens placed. Step 5. Only row 3, column 4 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 4, the rest of the blue region and every square adjacent to it — diagonals included.
Step 6. All of the mint region's remaining squares (3 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 7. Wherever orange ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
The board after step 7 — 4 of 10 queens placed. Step 8. All of the sea green region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 9. The khaki region has 4 squares left, spread across rows 7–10, columns 2 and 3. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 10. Here is the pairing argument. The orange and sea green regions have no open squares outside rows 9 and 10 — 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: 2 squares come off in one stroke.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: column 3 is down to one square, putting a queen on row 6, column 3; khaki has one square left, so its queen takes row 8, column 2; sea green has one square left, so its queen takes row 10, column 1; orange has one square left, so its queen takes row 9, column 6; pale yellow has one square left, so its queen takes row 7, column 5; mint has one square left, so its queen takes row 4, 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 4, column 9.
The board after step 11 — 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 #278
Board #278 of the 10x10 bank carries a easy rating. Its 100 squares are shared between ten colored regions, and the solution places ten queens: one per row, one per column, one per region, none of them side by side or corner to corner.
Like every board on this site, #278 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 #278 are: slate (1 square), amber (2 squares), sea green (2 squares), indigo (8 squares), khaki (8 squares), orange (9 squares), blue (11 squares), pale yellow (16 squares), mint (18 squares), red (25 squares). An even split would hand every color 10 squares, so the slate region is running 9 squares under that average while the red region is the roomiest area on the grid with 25 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 slate, with 1 square, is under far more pressure than red with 25. A 24-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. Amber is the tidiest shape on #278, packing 100% of its 1×2 bounding box, whereas pale yellow straggles across its 5×7 box at just 46%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Here is the full footprint of every color on puzzle #278, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Slate occupies 1 square within rows 5–5, columns 7–7. It never leaves row 5, so its queen is locked to that row.
Amber: 2 squares across rows 2–2, columns 9–10. It never leaves row 2, so its queen is locked to that row.
Sea green covers 2 squares, spanning 2 rows and 1 column (rows 9–10, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Indigo occupies 8 squares within rows 1–3, columns 6–10.
Khaki: 8 squares across rows 7–10, columns 1–3.
Orange covers 9 squares, spanning 2 rows and 6 columns (rows 9–10, columns 4–9).
Blue occupies 11 squares within rows 1–3, columns 1–6.
Pale yellow: 16 squares across rows 6–10, columns 4–10.
Mint covers 18 squares, spanning 5 rows and 5 columns (rows 3–7, columns 6–10).
Red occupies 25 squares within rows 2–8, columns 1–6.
Where to start on this board
The most constrained color is where a solve should begin, and on #278 that is slate with 1 square. It reaches from row 5 to row 5 and from column 7 to column 7 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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, sea green and orange 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 #278
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 2 colors. Columns 2 and 3 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 9 rows. Row 10 is the crowded extreme at 4 colors — worth revisiting later, not now.
Working through the middle game
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
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.
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 #278 is rated easy
The rating reflects how much the board concedes up front. Puzzle #278 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 24 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a easy board from the rest.
If #278 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.
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 #278, start hunting for it near row 1.
A non-spoiling distribution check: solved, #278 carries 3 queens on the perimeter against 7 queens inside, 1 of them cornered. 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 10x10 Queens puzzle #278?
Puzzle #278 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #278 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #278, 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 #278?
Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.