7x7 Queens Puzzle #292
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #292
What follows is a complete solve of puzzle #292, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 7 queen placements and 9 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 line confined to one region.
Techniques this board needs: region confined to one line, region shadow, last square in a region, line confined to one region, last square in a column.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 7 squares in all.
Step 2. All of the blue 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 3. The mint region has 5 squares left, spread across rows 4–6, columns 3–5. 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. Wherever slate ends up among its 4 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 — 0 of 7 queens placed. Step 5. Pale yellow is down to 5 candidates in rows 6 and 7, columns 2, 4, 5, 6, and 7, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 6. The slate region has 2 squares left, spread across rows 4 and 5, columns 2 and 3. 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 7. Only row 3, column 1 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 1, in blue and in the ring around that square is now dead.
Step 8. Mint is down to 3 candidates in rows 4–6, columns 4 and 5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 9. Row 7 has only pale yellow squares left (4 open squares). The row needs a queen and only pale yellow can provide one, which pins that colour to this row and kills its squares elsewhere: 1 square.
The board after step 9 — 1 of 7 queens placed. Step 10. Column 2 now has exactly one open square, row 5, column 2, in the slate region. Columns must each hold a queen, so that placement is forced. That clears row 5, column 2, the rest of the slate region and every square adjacent to it — diagonals included.
Step 11. Scan column 3 and only row 2, column 3 remains — a amber square. Every column takes a queen, so it takes this one. Cross out the whole of row 2 and column 3, the remaining amber squares, and the ring of neighbours around row 2, column 3.
Step 12. The mint region has 2 squares left, spread across rows 4 and 6, columns 4 and 5. 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 13. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: column 4 is down to one square, putting a queen on row 4, column 4; column 5 is down to one square, putting a queen on row 7, column 5; red has one square left, so its queen takes row 6, column 7; indigo has one square left, so its queen takes row 1, column 6. 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 6.
The board after step 13 — 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 #292
This is puzzle number 292 in the 7x7 collection, rated easy. 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 #292, 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 #292 are: indigo (2 squares), blue (2 squares), mint (5 squares), red (6 squares), pale yellow (7 squares), slate (9 squares), amber (18 squares). An even split would hand every color 7 squares, so the indigo region is running 5 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. Indigo is working with 2 squares while amber has 18 to spare, a gap of 16. Attack the cramped end and the roomy regions tend to resolve themselves.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×2 box, and mint the most diffuse at 56% of its 3×3 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Here is the full footprint of every color on puzzle #292, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo covers 2 squares, spanning 1 row and 2 columns (rows 1–1, columns 6–7). It never leaves row 1, so its queen is locked to that row.
Blue occupies 2 squares within rows 3–4, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Mint: 5 squares across rows 4–6, columns 3–5.
Red covers 6 squares, spanning 3 rows and 2 columns (rows 4–6, columns 6–7).
Pale yellow occupies 7 squares within rows 6–7, columns 2–7.
Slate: 9 squares across rows 3–7, columns 1–3.
Amber covers 18 squares, spanning 4 rows and 7 columns (rows 1–4, columns 1–7).
Where to start on this board
Open on the tightest color. Here that is indigo, confined to 2 squares between rows 1 and 1 and columns 6 and 7. Its queen has nowhere else to go, which means those 1 row and 2 columns carry more constraint than anywhere else on #292.
Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Blue 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 #292
A quick way to find the next move is to count how many different colors touch each line. On this board, row 2 is the narrowest, touched by only 1 color. Columns 1, 2, 4 and 5 are the tightest columns, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 1 color, so one of that handful must take the row and the rest are squeezed into the other 6 rows. Row 4 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
The middle of #292 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.
Two checks, run alternately, will carry you through the 49 squares of this grid. First: has any of the seven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 7x7 boards almost always run one of those checks and forget the other.
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 #292 is rated easy
The rating reflects how much the board concedes up front. Puzzle #292 has two regions confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 1 color, and the gap between its largest and smallest regions is 16 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.
Stuck on #292 despite the easy 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.
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 row 2 on this board.
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 #292?
Puzzle #292 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 1 color, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #292 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #292, 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 #292?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–1 and columns 6–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.