7x7 Queens Puzzle #247
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 17-step reasoning is written out below.
Previous puzzle · All 7x7 puzzles · Next puzzle
Step-by-step solution for puzzle #247
What follows is a complete solve of puzzle #247, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 7 queen placements and 10 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 proof by contradiction.
Techniques this board needs: last square in a region, region shadow, line confined to one region, pairing argument on rows, region confined to one line, proof by contradiction, last square in a row, last square in a column.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Only row 7, column 1 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 1, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 2. Amber is down to 5 candidates in rows 2–4, columns 2–4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The blue region has 4 squares left, spread across rows 1–3, 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 4. Wherever slate 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.
The board after step 4 — 1 of 7 queens placed. Step 5. Amber is down to 4 candidates in rows 2 and 3, columns 2–4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 6. Every open square left in column 5 (5 open squares) belongs to the mint region. Since that column must contain a queen, mint is the colour that supplies it — so mint squares anywhere else on the board are out, 4 squares in all.
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 2 squares at once.
Step 8. All of the mint region's remaining squares (3 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
The board after step 8 — 1 of 7 queens placed. Step 9. Test row 1, column 3 for indigo: place a queen there, run the forced consequences through, and column 4 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 10. All of the indigo region's remaining squares (2 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 11. Amber is down to 3 candidates in rows 2 and 3, columns 3 and 4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 12. 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: row 4 is down to one square, putting a queen on row 4, column 5; column 4 is down to one square, putting a queen on row 2, column 4; 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 7; red has one square left, so its queen takes row 6, column 6; slate has one square left, so its queen takes row 5, 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 5, column 3.
The board after step 12 — 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 #247
7x7 puzzle #247 is rated hard. Seven colored regions cover its 49 squares, and your job is to seat seven queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Puzzle #247 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #247 are: pale yellow (1 square), blue (4 squares), indigo (6 squares), red (6 squares), amber (7 squares), slate (11 squares), mint (14 squares). An even split would hand every color 7 squares, so the pale yellow region is running 6 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 13 square difference between pale yellow 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 100% of its 2×3 box, and amber the most diffuse at 58% of its 3×4 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.
Pale yellow covers 1 square, spanning 1 row and 1 column (rows 7–7, columns 1–1). It never leaves row 7, so its queen is locked to that row.
Blue occupies 4 squares within rows 1–3, columns 6–7.
Indigo: 6 squares across rows 1–2, columns 1–3.
Red covers 6 squares, spanning 4 rows and 2 columns (rows 4–7, columns 6–7).
Amber occupies 7 squares within rows 2–4, columns 1–4.
Slate: 11 squares across rows 4–7, columns 1–4.
Mint covers 14 squares, spanning 7 rows and 3 columns (rows 1–7, columns 4–6).
Where to start on this board
The most constrained color is where a solve should begin, and on #247 that is pale yellow with 1 square. It reaches from row 7 to row 7 and from column 1 to column 1 — 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 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 #247
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3, 5 and 6 are the narrowest, touched by only 3 colors. Column 5 is the tightest column, with 1 color.
A line with few colors is a line close to resolving. Where only 3 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 4 colors — worth revisiting later, not now.
Working through the middle game
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
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.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #247 is rated hard
Ratings track how generous the opening is. On #247 you get two regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 13-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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 #247 is column 5.
A non-spoiling distribution check: solved, #247 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 7x7 Queens puzzle #247?
Puzzle #247 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #247 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #247, 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 #247?
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.