7x7 Queens Puzzle #260
Difficulty: medium. 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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #260
What follows is a complete solve of puzzle #260, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 7 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 region shadow.
Techniques this board needs: region shadow, region confined to one line, last square in a region.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Wherever indigo ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. Amber is down to 5 candidates in rows 1–4, columns 6 and 7, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The indigo region has 5 squares left, spread across rows 1 and 2, columns 3–6. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 4. All of the blue region's remaining squares (3 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
The board after step 4 — 0 of 7 queens placed. Step 5. Indigo is down to 4 candidates in rows 1 and 2, columns 3–6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
Step 6. The amber region has 3 squares left, spread across rows 1, 2, and 4, columns 6 and 7. 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 7. Only row 5, column 6 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 6, in slate and in the ring around that square is now dead.
The board after step 7 — 1 of 7 queens placed. Step 8. All of the amber 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 9. Only row 7, column 5 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 5, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 10. Wherever indigo ends up among its 2 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 11. 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: blue has one square left, so its queen takes row 3, column 3; indigo has one square left, so its queen takes row 1, column 4; amber has one square left, so its queen takes row 2, column 7; mint has one square left, so its queen takes row 4, column 1; red has one square left, so its queen takes row 6, column 2. 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 2.
The board after step 11 — 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 #260
This is puzzle number 260 in the 7x7 collection, rated medium. The grid holds 49 squares split between seven colored regions, and a finished board carries seven queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
There is exactly one way to finish #260, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these seven regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #260 are: slate (3 squares), blue (4 squares), amber (5 squares), indigo (6 squares), pale yellow (8 squares), red (9 squares), mint (14 squares). An even split would hand every color 7 squares, so the slate region is running 4 squares under that average while the mint region is the roomiest area on the grid with 14 squares.
Every color takes one queen and one only, whatever its size — which is why the 11 square difference between slate and mint 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.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 75% of its 2×4 box, and mint the most diffuse at 56% of its 5×5 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.
Slate occupies 3 squares within rows 4–5, columns 6–7.
Blue: 4 squares across rows 2–3, columns 3–5.
Amber covers 5 squares, spanning 4 rows and 2 columns (rows 1–4, columns 6–7).
Indigo occupies 6 squares within rows 1–2, columns 3–6.
Pale yellow: 8 squares across rows 5–7, columns 4–7.
Red covers 9 squares, spanning 3 rows and 4 columns (rows 5–7, columns 1–4).
Mint occupies 14 squares within rows 1–5, columns 1–5.
Where to start on this board
Open on the tightest color. Here that is slate, confined to 3 squares between rows 4 and 5 and columns 6 and 7. Its queen has nowhere else to go, which means those 2 rows and 2 columns carry more constraint than anywhere else on #260.
Slate 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 and blue 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 #260
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 6 and 7 are the narrowest, touched by only 2 colors. Columns 1 and 2 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 2 colors, so one of that handful must take the row and the rest are squeezed into the other 6 rows. Row 5 sits at the far end with 4 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 seven colors looking for one with a single square left; sweep the seven rows and seven columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 7x7 solve from a stalled one.
Resist the plausible-looking queen. On #260 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #260 is rated medium
Ratings track how generous the opening is. On #260 you get no region pinned to a single row or column, a smallest color of 3 squares, a tightest row crossed by 2 colors, and a 11-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.
Stuck on #260 despite the medium rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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.
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 #260 is row 6.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 3 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 7x7 Queens puzzle #260?
Puzzle #260 is rated medium. Its smallest color region holds 3 squares, its tightest row is touched by 2 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 7x7 puzzle #260 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #260, 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 #260?
Start with the slate region — the most constrained color on this board, with 3 squares spanning rows 4–5 and columns 6–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.