7x7 Queens Puzzle #266
Difficulty: hard. 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 8-step reasoning is written out below.
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Step-by-step solution for puzzle #266
What follows is a complete solve of puzzle #266, worked the way a person works it rather than the way a computer does. It runs to 8 deductions — 7 queen placements and 1 elimination step 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: last square in a region, region shadow.
Show the full walkthrough (5 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: pale yellow has one square left, so its queen takes row 7, column 1; slate has one square left, so its queen takes row 5, column 2; mint has one square left, so its queen takes row 4, column 4; indigo has one square left, so its queen takes row 1, column 3. 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 1, column 3.
Step 2. Amber is down to 2 candidates in rows 2 and 3, columns 5 and 6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The blue region is down to one open square, at row 3, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 7, the remaining blue squares, and the ring of neighbours around row 3, column 7.
The board after step 3 — 5 of 7 queens placed. Step 4. Only row 2, column 5 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 5, in amber and in the ring around that square is now dead.
Step 5. 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. Row 6 and column 6 are now spoken for, along with the squares touching that queen.
The board after step 5 — 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 #266
Board #266 of the 7x7 bank carries a hard 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, #266 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 #266 are: pale yellow (1 square), blue (4 squares), slate (4 squares), indigo (6 squares), mint (9 squares), amber (12 squares), red (13 squares). An even split would hand every color 7 squares, so the pale yellow region is running 6 squares under that average while the red region is the roomiest area on the grid with 13 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Pale yellow has only 1 place to put its queen; red has 13. The spread between them on this board is 12 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Look at arrangement as well as area. Pale yellow is the densest region on this grid at 100% of a 1×1 frame; amber is the loosest, occupying only 60% of its 4×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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.
Pale yellow occupies 1 square within rows 7–7, columns 1–1. It never leaves row 7, so its queen is locked to that row.
Blue: 4 squares across rows 2–4, columns 6–7.
Slate covers 4 squares, spanning 3 rows and 2 columns (rows 5–7, columns 1–2).
Indigo occupies 6 squares within rows 1–2, columns 1–4.
Mint: 9 squares across rows 3–5, columns 1–4.
Amber covers 12 squares, spanning 4 rows and 5 columns (rows 1–4, columns 3–7).
Red occupies 13 squares within rows 5–7, columns 3–7.
Where to start on this board
Begin where the choices are fewest. On this board that means pale yellow, which owns just 1 square inside a 1×1 window running from row 7 to row 7 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because pale yellow never leaves row 7, its queen must be in that row — and that instantly settles row 7 for everyone else. Sweep along it and X out every square that is not pale yellow. 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. 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 #266
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 6 are the narrowest, touched by only 2 colors. Column 5 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 6 rows. Row 7 is the crowded extreme at 3 colors — worth revisiting later, not now.
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.
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 #266 is rated hard
Ratings track how generous the opening is. On #266 you get two regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 12-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a hard board from the rest.
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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #266 the place to look for one is around row 1.
A non-spoiling distribution check: solved, #266 carries 3 queens on the perimeter against 4 queens inside, 1 of them cornered. 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 7x7 Queens puzzle #266?
Puzzle #266 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 7x7 puzzle #266 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #266, 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 #266?
Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.