7x7 Queens Puzzle #272
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 11-step reasoning is written out below.
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Step-by-step solution for puzzle #272
What follows is a complete solve of puzzle #272, worked the way a person works it rather than the way a computer does. It runs to 11 deductions — 7 queen placements and 4 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 pairing argument on rows.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows.
Show the full walkthrough (6 steps) — contains the solution
Step 1. Only row 4, column 3 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 3, the rest of the mint region and every square adjacent to it — diagonals included.
Step 2. 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: 6 squares come off.
Step 3. The indigo region has 3 squares left, spread across rows 1 and 2, 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.
The board after step 3 — 1 of 7 queens placed. Step 4. Wherever pale yellow 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.
Step 5. Indigo and amber are now boxed into rows 1 and 2 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 4 squares at once.
Step 6. 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: blue has one square left, so its queen takes row 3, column 1; 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; 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; 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 6 — 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 #272
This is puzzle number 272 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 #272, 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 #272 are: mint (1 square), amber (2 squares), indigo (5 squares), pale yellow (6 squares), blue (10 squares), red (10 squares), slate (15 squares). An even split would hand every color 7 squares, so the mint region is running 6 squares under that average while the slate region is the roomiest area on the grid with 15 squares.
Every color takes one queen and one only, whatever its size — which is why the 14 square difference between mint and slate 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 amber is the most solid, filling 100% of its 2×1 box, and pale yellow the most diffuse at 50% 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.
Mint occupies 1 square within rows 4–4, columns 3–3. It never leaves row 4, so its queen is locked to that row.
Amber: 2 squares across rows 1–2, columns 7–7. It sits wholly inside column 7, so its queen must be in that column.
Indigo covers 5 squares, spanning 2 rows and 3 columns (rows 1–2, columns 4–6).
Pale yellow occupies 6 squares within rows 5–7, columns 3–6.
Blue: 10 squares across rows 1–4, columns 1–4.
Red covers 10 squares, spanning 3 rows and 4 columns (rows 5–7, columns 1–4).
Slate occupies 15 squares within rows 3–7, columns 2–7.
Where to start on this board
Open on the tightest color. Here that is mint, confined to 1 square between rows 4 and 4 and columns 3 and 3. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #272.
Because mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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 and amber 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 #272
A quick way to find the next move is to count how many different colors touch each line. On this board, row 3 is the narrowest, touched by only 2 colors. Columns 1 and 7 are the tightest columns, 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
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
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.
Resist the plausible-looking queen. On #272 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 #272 is rated medium
Ratings track how generous the opening is. On #272 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 14-square gap between the largest and smallest regions. Those four numbers largely explain the medium 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 medium board from the rest.
Stuck on #272 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 #272 is row 3.
A non-spoiling distribution check: solved, #272 carries 4 queens on the perimeter against 3 queens inside, with the corners empty. 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 #272?
Puzzle #272 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #272 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #272, 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 #272?
Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.