10x10 Queens Puzzle #290
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.
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Step-by-step solution for puzzle #290
What follows is a complete solve of puzzle #290, 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: 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 (13 steps) — contains the solution
Step 1. Only row 10, column 5 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 5, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 2. Indigo is down to 6 candidates in rows 1–3, columns 1–3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
Step 3. The amber region has 3 squares left, spread across rows 1 and 2, columns 7 and 8. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
Step 4. Wherever blue 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 4 — 1 of 10 queens placed. Step 5. Mint is down to 4 candidates in rows 3–5, columns 1 and 2, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about mint itself.
Step 6. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 7. Indigo, amber, and blue are now boxed into rows 1–3 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 10 squares at once.
Step 8. All of the mint 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. 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: orange has one square left, so its queen takes row 9, column 3; indigo has one square left, so its queen takes row 1, column 2; blue has one square left, so its queen takes row 3, column 9; amber has one square left, so its queen takes row 2, column 7; slate has one square left, so its queen takes row 5, column 10; mint has one square left, so its queen takes row 4, 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 4, column 1.
The board after step 9 — 7 of 10 queens placed. Step 10. Red cannot leave row 6 — every one of its open squares (2 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 1 square in all.
Step 11. Column 4 now has exactly one open square, row 7, column 4, in the pale yellow region. Columns must each hold a queen, so that placement is forced. Everything else in row 7, in column 4, in pale yellow and in the ring around that square is now dead.
Step 12. Only row 8, column 8 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 8, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 13. The red region is down to one open square, at row 6, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 6, the remaining red squares, and the ring of neighbours around row 6, column 6.
The board after step 13 — 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 #290
Board #290 of the 10x10 bank carries a hard 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.
As with every puzzle in this collection, #290 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 #290 are: sea green (1 square), amber (3 squares), blue (4 squares), mint (5 squares), indigo (6 squares), orange (7 squares), slate (12 squares), red (16 squares), khaki (19 squares), pale yellow (27 squares). An even split would hand every color 10 squares, so the sea green region is running 9 squares under that average while the pale yellow region is the roomiest area on the grid with 27 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 sea green, with 1 square, is under far more pressure than pale yellow with 27. A 26-square gap like this one rewards players who start where the choices are fewest.
Shape matters as much as size. The sea green region is the most compact color here, filling 100% of the 1×1 box that encloses it, while red is the most scattered at 53% of its 6×5 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
Region by region
Here is the full footprint of every color on puzzle #290, 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 occupies 1 square within rows 10–10, columns 5–5. It never leaves row 10, so its queen is locked to that row.
Amber: 3 squares across rows 1–2, columns 7–8.
Blue covers 4 squares, spanning 3 rows and 2 columns (rows 1–3, columns 9–10).
Mint occupies 5 squares within rows 2–5, columns 1–2.
Indigo: 6 squares across rows 1–3, columns 1–3.
Orange covers 7 squares, spanning 2 rows and 4 columns (rows 9–10, columns 1–4).
Slate occupies 12 squares within rows 2–6, columns 7–10.
Red: 16 squares across rows 1–6, columns 4–8.
Khaki covers 19 squares, spanning 5 rows and 6 columns (rows 6–10, columns 5–10).
Pale yellow occupies 27 squares within rows 3–9, columns 1–7.
Where to start on this board
The most constrained color is where a solve should begin, and on #290 that is sea green with 1 square. It reaches from row 10 to row 10 and from column 5 to column 5 — 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 sea green never leaves row 10, its queen must be in that row — and that instantly settles row 10 for everyone else. Sweep along it and X out every square that is not sea green. 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 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 #290
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 7 and 8 are the narrowest, touched by only 2 colors. Columns 3, 4, 6, 9 and 10 are the tightest columns, with 3 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 9 rows. Row 3, meeting 6 colors, is the opposite case — the busiest line on #290 and the last one you should expect to crack.
Working through the middle game
The middle of #290 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.
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.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #290 is rated hard
The rating reflects how much the board concedes up front. Puzzle #290 has two 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 26 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
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 #290, start hunting for it near row 7.
Here is a shape check that gives nothing away: when #290 is solved, 4 queens sit on the outer edge of the grid and 6 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #290?
Puzzle #290 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #290 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #290, 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 #290?
Start with the sea green region — the most constrained color on this board, with 1 square spanning rows 10–10 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.