8x8 Queens Puzzle #273
Difficulty: hard. Place 8 queens on this 8x8 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.
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Step-by-step solution for puzzle #273
What follows is a complete solve of puzzle #273, worked the way a person works it rather than the way a computer does. It runs to 12 deductions — 8 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 columns.
Techniques this board needs: last square in a region, region shadow, pairing argument on columns, region confined to one line.
Show the full walkthrough (7 steps) — contains the solution
Step 1. Only row 8, column 1 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 1, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 2. The red region is down to one open square, at row 6, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 2, the remaining red squares, and the ring of neighbours around row 6, column 2.
Step 3. The blue region has 5 squares left, spread across rows 3–5, 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. Here is the pairing argument. The amber and slate regions have no open squares outside columns 7 and 8 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 4 squares come off in one stroke.
The board after step 4 — 2 of 8 queens placed. Step 5. Mint is down to 5 candidates in rows 1–5, columns 5 and 6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 6. All of the pale yellow region's remaining squares (3 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
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: slate has one square left, so its queen takes row 5, column 8; amber has one square left, so its queen takes row 2, column 7; mint has one square left, so its queen takes row 4, column 6; blue has one square left, so its queen takes row 3, column 4; 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 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.
The board after step 7 — 8 of 8 queens placed.
That completes the board: 8 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 8x8 Queens puzzle #273
Puzzle #273 is one of the hard-rated boards in the 8x8 set. Eight colors divide its 64 squares, and you win by placing eight queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
There is exactly one way to finish #273, 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 eight regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #273 are: khaki (1 square), amber (5 squares), red (5 squares), slate (7 squares), mint (8 squares), indigo (10 squares), blue (14 squares), pale yellow (14 squares). An even split would hand every color 8 squares, so the khaki region is running 7 squares under that average while the pale yellow region is the roomiest area on the grid with 14 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 khaki, with 1 square, is under far more pressure than pale yellow with 14. A 13-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Khaki is the densest region on this grid at 100% of a 1×1 frame; pale yellow is the loosest, occupying only 47% of its 5×6 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a hard board.
Khaki: 1 square across rows 8–8, columns 1–1. It never leaves row 8, so its queen is locked to that row.
Amber covers 5 squares, spanning 4 rows and 2 columns (rows 1–4, columns 7–8).
Red occupies 5 squares within rows 5–7, columns 1–2.
Slate: 7 squares across rows 5–8, columns 7–8.
Mint covers 8 squares, spanning 5 rows and 3 columns (rows 1–5, columns 5–7).
Indigo occupies 10 squares within rows 1–3, columns 1–5.
Blue: 14 squares across rows 2–6, columns 1–5.
Pale yellow covers 14 squares, spanning 5 rows and 6 columns (rows 4–8, columns 2–7).
Where to start on this board
Open on the tightest color. Here that is khaki, confined to 1 square between rows 8 and 8 and columns 1 and 1. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #273.
Because khaki never leaves row 8, its queen must be in that row — and that instantly settles row 8 for everyone else. Sweep along it and X out every square that is not khaki. 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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: amber, red and slate span only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.
The tightest lines on puzzle #273
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 7 and 8 are the narrowest, touched by only 3 colors. Columns 6 and 8 are the tightest columns, with 2 colors.
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 7 rows. Row 5, meeting 5 colors, is the opposite case — the busiest line on #273 and the last one you should expect to crack.
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 64 squares of this grid. First: has any of the eight regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 8x8 boards almost always run one of those checks and forget the other.
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 #273 is rated hard
The hard label comes out of four measurable things about #273: two of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 13. Boards that score tight on those measures give up their first queen fast.
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.
Stuck on #273 despite the hard 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 8x8
At 8x8 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 #273, start hunting for it near column 6.
Here is a shape check that gives nothing away: when #273 is solved, 3 queens sit on the outer edge of the grid and 5 sit inside it, with 1 queen 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.
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Questions about this puzzle
How hard is 8x8 Queens puzzle #273?
Puzzle #273 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 8x8 puzzle #273 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #273, has been verified to have exactly one valid arrangement of eight queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #273?
Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.