7x7 Queens Puzzle #10
Difficulty: easy. Place 7 queens on this 7x7 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 10-step reasoning is written out below.
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Step-by-step solution for puzzle #10
What follows is a complete solve of puzzle #10, worked the way a person works it rather than the way a computer does. It runs to 10 deductions — 7 queen placements and 3 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 confined to one line.
Techniques this board needs: last square in a region, region confined to one line.
Show the full walkthrough (6 steps) — contains the solution
Step 1. Only row 3, column 6 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 6, the rest of the blue region and every square adjacent to it — diagonals included.
Step 2. The pale yellow region is down to one open square, at row 7, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 2, the remaining pale yellow squares, and the ring of neighbours around row 7, column 2.
Step 3. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 3 squares in all.
The board after step 3 — 2 of 7 queens placed. Step 4. All of the slate region's remaining squares (2 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.
Step 5. Indigo cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to indigo, so every square in it owned by another colour is dead: 1 square in all.
Step 6. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: red has one square left, so its queen takes row 6, column 4; indigo has one square left, so its queen takes row 1, column 5; mint has one square left, so its queen takes row 4, column 3; slate has one square left, so its queen takes row 5, column 7; amber has one square left, so its queen takes row 2, 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 2, column 1.
The board after step 6 — 7 of 7 queens placed.
That completes the board: 7 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 7x7 Queens puzzle #10
Board #10 of the 7x7 bank carries a easy rating. Its 49 squares are shared between seven colored regions, and the solution places seven 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, #10 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 #10 are: blue (1 square), pale yellow (1 square), mint (2 squares), slate (6 squares), red (10 squares), indigo (11 squares), amber (18 squares). An even split would hand every color 7 squares, so the blue region is running 6 squares under that average while the amber region is the roomiest area on the grid with 18 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Blue is working with 1 square while amber has 18 to spare, a gap of 17. Attack the cramped end and the roomy regions tend to resolve themselves.
Square count is only half the story — how a color is arranged counts too. Blue is the tidiest shape on #10, packing 100% of its 1×1 bounding box, whereas indigo straggles across its 5×4 box at just 55%. 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 #10, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Blue covers 1 square, spanning 1 row and 1 column (rows 3–3, columns 6–6). It never leaves row 3, so its queen is locked to that row.
Pale yellow occupies 1 square within rows 7–7, columns 2–2. It never leaves row 7, so its queen is locked to that row.
Mint: 2 squares across rows 4–4, columns 3–4. It never leaves row 4, so its queen is locked to that row.
Slate covers 6 squares, spanning 4 rows and 2 columns (rows 4–7, columns 6–7).
Red occupies 10 squares within rows 5–7, columns 3–6.
Indigo: 11 squares across rows 1–5, columns 4–7.
Amber covers 18 squares, spanning 7 rows and 4 columns (rows 1–7, columns 1–4).
Where to start on this board
Begin where the choices are fewest. On this board that means blue, which owns just 1 square inside a 1×1 window running from row 3 to row 3 and column 6 to column 6. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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. Mint and pale yellow 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 #10
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 2 are the narrowest, touched by only 2 colors. Column 1 is the tightest column, with 1 color.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 6 rows. By contrast row 7 meets 4 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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 seven 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 7x7 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 #10 is rated easy
The rating reflects how much the board concedes up front. Puzzle #10 has five 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 17 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.
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 7x7
At 7x7 the whole grid stays within a single glance, which makes systematic scanning practical. Read the rows in order and count the colors in each — a row touched by two colors is far more constrained than one touched by five, and that is usually where the next forced move hides. The board is small enough that re-scanning from the top after each placement costs almost nothing.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around column 1 on this board.
As a sanity check rather than a spoiler: the finished solution to #10 puts 4 queens on the outer border and 3 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 7x7 Queens puzzle #10?
Puzzle #10 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #10 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #10, has been verified to have exactly one valid arrangement of seven queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #10?
Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.