7x7 Queens Puzzle #276
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 12-step reasoning is written out below.
Previous puzzle · All 7x7 puzzles · Next puzzle
Step-by-step solution for puzzle #276
What follows is a complete solve of puzzle #276, worked the way a person works it rather than the way a computer does. It runs to 12 deductions — 7 queen placements and 5 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, last square in a region, line confined to one region, last square in a column.
Show the full walkthrough (7 steps) — contains the solution
Step 1. Amber cannot leave column 7 — every one of its open squares (4 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 3 squares in all.
Step 2. All of the red region's remaining squares (2 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 9 squares come off.
Step 3. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 5 squares in all.
Step 4. All of the slate region's remaining squares (2 open squares) lie in row 5. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
The board after step 4 — 0 of 7 queens placed. Step 5. Only row 6, column 3 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 3, the rest of the red region and every square adjacent to it — diagonals included.
Step 6. Every open square left in column 1 (4 open squares) belongs to the blue region. Since that column must contain a queen, blue is the colour that supplies it — so blue squares anywhere else on the board are out, 3 squares in all.
Step 7. 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: column 2 is down to one square, putting a queen on row 1, column 2; column 4 is down to one square, putting a queen on row 4, column 4; blue has one square left, so its queen takes row 3, column 1; amber has one square left, so its queen takes row 2, column 7; slate has one square left, so its queen takes row 5, column 6; pale yellow has one square left, so its queen takes row 7, column 5. 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 7, column 5.
The board after step 7 — 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 #276
This is puzzle number 276 in the 7x7 collection, rated hard. 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.
Like every board on this site, #276 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #276 are: red (2 squares), pale yellow (3 squares), amber (4 squares), indigo (6 squares), slate (10 squares), mint (11 squares), blue (13 squares). An even split would hand every color 7 squares, so the red region is running 5 squares under that average while the blue region is the roomiest area on the grid with 13 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So red, with 2 squares, is under far more pressure than blue with 13. A 11-square gap like this one rewards players who start where the choices are fewest.
A region's outline can constrain it more than its size does. Here amber is the most solid, filling 100% of its 4×1 box, and slate the most diffuse at 67% of its 3×5 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.
Red: 2 squares across rows 5–6, columns 3–3. It sits wholly inside column 3, so its queen must be in that column.
Pale yellow covers 3 squares, spanning 1 row and 3 columns (rows 7–7, columns 5–7). It never leaves row 7, so its queen is locked to that row.
Amber occupies 4 squares within rows 1–4, columns 7–7. It sits wholly inside column 7, so its queen must be in that column.
Indigo: 6 squares across rows 1–3, columns 2–4.
Slate covers 10 squares, spanning 3 rows and 5 columns (rows 5–7, columns 3–7).
Mint occupies 11 squares within rows 1–4, columns 3–6.
Blue: 13 squares across rows 1–7, columns 1–2.
Where to start on this board
Open on the tightest color. Here that is red, confined to 2 squares between rows 5 and 6 and columns 3 and 3. Its queen has nowhere else to go, which means those 2 rows and 1 column carry more constraint than anywhere else on #276.
Because red stays inside column 3, its queen belongs to that column and no other region may use it. Cross out the rest of column 3 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
Work outward to the other flat regions next. Pale yellow 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 #276
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 4, 5, 6 and 7 are the narrowest, touched by only 3 colors. Column 1 is the tightest column, with 1 color.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 6 rows. Row 3, meeting 4 colors, is the opposite case — the busiest line on #276 and the last one you should expect to crack.
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 #276 is rated hard
Ratings track how generous the opening is. On #276 you get three regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 3 colors, and a 11-square gap between the largest and smallest regions. Those four numbers largely explain the hard 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.
If #276 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #276, start hunting for it near column 1.
Here is a shape check that gives nothing away: when #276 is solved, 4 queens sit on the outer edge of the grid and 3 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #276?
Puzzle #276 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #276 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #276, 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 #276?
Start with the red region — the most constrained color on this board, with 2 squares spanning rows 5–6 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.