10x10 Queens Puzzle #280
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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #280
What follows is a complete solve of puzzle #280, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 10 queen placements and 7 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 columns.
Techniques this board needs: region shadow, region confined to one line, pairing argument on columns, last square in a region, last square in a row.
Show the full walkthrough (8 steps) — contains the solution
Step 1. Wherever indigo 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. Blue is down to 4 candidates in rows 3–5, columns 5 and 6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 3. The mint region has 3 squares left, spread across rows 3 and 4, columns 9 and 10. 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 4. All of the indigo region's remaining squares (3 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 7 squares come off.
The board after step 4 — 0 of 10 queens placed. Step 5. Sea green is down to 3 candidates in rows 9 and 10, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about sea green itself.
Step 6. Here is the pairing argument. The slate and sea green regions have no open squares outside columns 1 and 2 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 7 squares come off in one stroke.
Step 7. Indigo, mint, and pale yellow are now boxed into columns 8–10 and nothing else. That is 3 colours needing 3 columns, so they fill those columns between them — which locks every remaining colour out and removes 11 squares at once.
Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 10 queens fall out in order without any new idea being needed: orange has one square left, so its queen takes row 9, column 7; red has one square left, so its queen takes row 6, column 6; blue has one square left, so its queen takes row 3, column 5; mint has one square left, so its queen takes row 4, column 10; pale yellow has one square left, so its queen takes row 7, column 9; indigo has one square left, so its queen takes row 1, column 8; row 2 is down to one square, putting a queen on row 2, column 3; row 5 is down to one square, putting a queen on row 5, column 1; 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 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 8, column 4.
The board after step 8 — 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 #280
This is puzzle number 280 in the 10x10 collection, rated medium. The grid holds 100 squares split between ten colored regions, and a finished board carries ten queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
Like every board on this site, #280 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 #280 are: sea green (3 squares), indigo (4 squares), blue (4 squares), mint (4 squares), slate (8 squares), orange (10 squares), pale yellow (11 squares), red (14 squares), khaki (16 squares), amber (26 squares). An even split would hand every color 10 squares, so the sea green region is running 7 squares under that average while the amber region is the roomiest area on the grid with 26 squares.
Every color takes one queen and one only, whatever its size — which is why the 23 square difference between sea green and amber is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Look at arrangement as well as area. Slate is the densest region on this grid at 80% of a 5×2 frame; red is the loosest, occupying only 58% of its 8×3 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Here is the full footprint of every color on puzzle #280, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Sea green covers 3 squares, spanning 2 rows and 2 columns (rows 9–10, columns 1–2).
Indigo occupies 4 squares within rows 1–2, columns 8–10.
Blue: 4 squares across rows 3–5, columns 5–6.
Mint covers 4 squares, spanning 3 rows and 2 columns (rows 2–4, columns 9–10).
Slate occupies 8 squares within rows 5–9, columns 1–2.
Orange: 10 squares across rows 7–10, columns 7–10.
Pale yellow covers 11 squares, spanning 6 rows and 3 columns (rows 3–8, columns 8–10).
Red occupies 14 squares within rows 1–8, columns 6–8.
Khaki: 16 squares across rows 6–10, columns 3–7.
Amber covers 26 squares, spanning 7 rows and 5 columns (rows 1–7, columns 1–5).
Where to start on this board
Sea green is the natural opening on #280: it is the smallest region on the grid at 3 squares, boxed into rows 9–10 and columns 1–2. Since one of those squares must hold a queen, that block of 2 rows and 2 columns is the most contested part of the board.
Sea green 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 3 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. Indigo 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 #280
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 10 are the narrowest, touched by only 3 colors. Columns 3 and 4 are the tightest columns, with 2 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 7 sits at the far end with 6 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 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 #280 is rated medium
The rating reflects how much the board concedes up front. Puzzle #280 has no region confined to a single row or column, its smallest color holds 3 squares, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 23 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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 #280 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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #280 is column 3.
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 #280?
Puzzle #280 is rated medium. Its smallest color region holds 3 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 #280 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #280, 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 #280?
Start with the sea green region — the most constrained color on this board, with 3 squares spanning rows 9–10 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.