10x10 Queens Puzzle #281
Difficulty: medium. 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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #281
What follows is a complete solve of puzzle #281, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 10 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, last square in a region, region shadow.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Amber cannot leave column 10 — 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: 10 squares in all.
Step 2. All of the slate region's remaining squares (2 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 12 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: 10 squares in all.
The board after step 3 — 0 of 10 queens placed. Step 4. All of the sea green region's remaining squares (2 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 10 squares come off.
Step 5. Only row 7, column 7 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 7, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 6. The indigo region is down to one open square, at row 1, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 6, the remaining indigo squares, and the ring of neighbours around row 1, column 6.
The board after step 6 — 2 of 10 queens placed. Step 7. 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 8. Blue is down to 3 candidates in rows 3 and 4, columns 1, 3, and 4, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 9. 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: slate has one square left, so its queen takes row 5, column 2; khaki has one square left, so its queen takes row 8, column 9; mint has one square left, so its queen takes row 4, column 5; sea green has one square left, so its queen takes row 10, column 8; orange has one square left, so its queen takes row 9, column 1; blue has one square left, so its queen takes row 3, column 3; red has one square left, so its queen takes row 6, 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 6, column 4.
The board after step 9 — 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 #281
Puzzle #281 is one of the medium-rated boards in the 10x10 set. Ten colors divide its 100 squares, and you win by placing ten queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
As with every puzzle in this collection, #281 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #281 are: amber (2 squares), slate (2 squares), pale yellow (2 squares), sea green (2 squares), indigo (5 squares), orange (13 squares), blue (16 squares), red (16 squares), khaki (18 squares), mint (24 squares). An even split would hand every color 10 squares, so the amber region is running 8 squares under that average while the mint region is the roomiest area on the grid with 24 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 amber, with 2 squares, is under far more pressure than mint with 24. A 22-square gap like this one rewards players who start where the choices are fewest.
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 khaki the most diffuse at 60% of its 6×5 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 occupies 2 squares within rows 1–2, columns 10–10. It sits wholly inside column 10, so its queen must be in that column.
Slate: 2 squares across rows 4–5, columns 2–2. It sits wholly inside column 2, so its queen must be in that column.
Pale yellow covers 2 squares, spanning 1 row and 2 columns (rows 7–7, columns 7–8). It never leaves row 7, so its queen is locked to that row.
Sea green occupies 2 squares within rows 9–10, columns 8–8. It sits wholly inside column 8, so its queen must be in that column.
Indigo: 5 squares across rows 1–2, columns 6–9.
Orange covers 13 squares, spanning 6 rows and 3 columns (rows 5–10, columns 1–3).
Blue occupies 16 squares within rows 1–5, columns 1–5.
Red: 16 squares across rows 5–10, columns 3–6.
Khaki covers 18 squares, spanning 6 rows and 5 columns (rows 5–10, columns 6–10).
Mint occupies 24 squares within rows 2–6, columns 4–10.
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 1 to row 2 and column 10 to column 10. 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 10, its queen belongs to that column and no other region may use it. Cross out the rest of column 10 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, indigo, slate and sea green 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 #281
A quick way to find the next move is to count how many different colors touch each line. On this board, row 3 is the narrowest, touched by only 2 colors. Column 1 is the tightest column, with 2 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 5 is the crowded extreme at 6 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.
Keep alternating between two views of the board. In the region view you ask which of the ten colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 10x10 board unwinds.
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 #281 is rated medium
Ratings track how generous the opening is. On #281 you get four regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 22-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.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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 #281, start hunting for it near row 3.
A non-spoiling distribution check: solved, #281 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.
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Questions about this puzzle
How hard is 10x10 Queens puzzle #281?
Puzzle #281 is rated medium. Its smallest color region holds 2 squares, 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 #281 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #281, 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 #281?
Start with the amber region — the most constrained color on this board, with 2 squares spanning rows 1–2 and columns 10–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.