8x8 Queens Puzzle #269
Difficulty: medium. 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 19-step reasoning is written out below.
Previous puzzle · All 8x8 puzzles · Next puzzle
Step-by-step solution for puzzle #269
What follows is a complete solve of puzzle #269, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 8 queen placements and 11 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 confined to one line, region shadow, pairing argument on rows, pairing argument on columns, last square in a row.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 8, column 8 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 8, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 7 squares come off.
Step 3. The mint region has 5 squares left, spread across rows 3–6, columns 1 and 2. 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 red ends up among its 2 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
The board after step 4 — 1 of 8 queens placed. Step 5. Pale yellow is down to 3 candidates in rows 6 and 7, columns 4 and 5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 6. Here is the pairing argument. The red and pale yellow regions have no open squares outside rows 6 and 7 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 4 squares come off in one stroke.
Step 7. Mint cannot leave column 1 — every one of its open squares (3 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 2 squares in all.
Step 8. All of the slate region's remaining squares (3 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.
Step 9. Mint cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 1 square in all.
The board after step 9 — 1 of 8 queens placed. Step 10. Here is the pairing argument. The indigo and red regions have no open squares outside columns 6 and 7 — 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.
Step 11. Blue cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 4 squares in all.
Step 12. All of the pale yellow region's remaining squares (2 open squares) lie in column 4. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
Step 13. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 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 1; slate has one square left, so its queen takes row 5, column 3; amber has one square left, so its queen takes row 2, column 2; blue has one square left, so its queen takes row 3, column 5; pale yellow has one square left, so its queen takes row 7, column 4; 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 — 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 #269
Puzzle #269 is one of the medium-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 #269, 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 #269 are: khaki (1 square), mint (5 squares), indigo (6 squares), blue (7 squares), red (7 squares), slate (9 squares), pale yellow (9 squares), amber (20 squares). An even split would hand every color 8 squares, so the khaki region is running 7 squares under that average while the amber region is the roomiest area on the grid with 20 squares.
Every color takes one queen and one only, whatever its size — which is why the 19 square difference between khaki and amber 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.
Look at arrangement as well as area. Khaki is the densest region on this grid at 100% of a 1×1 frame; indigo is the loosest, occupying only 50% of its 4×3 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 medium board.
Khaki occupies 1 square within rows 8–8, columns 8–8. It never leaves row 8, so its queen is locked to that row.
Mint: 5 squares across rows 3–6, columns 1–2.
Indigo covers 6 squares, spanning 4 rows and 3 columns (rows 1–4, columns 6–8).
Blue occupies 7 squares within rows 2–4, columns 5–7.
Red: 7 squares across rows 5–8, columns 6–8.
Slate covers 9 squares, spanning 4 rows and 4 columns (rows 5–8, columns 1–4).
Pale yellow occupies 9 squares within rows 6–8, columns 3–6.
Amber: 20 squares across rows 1–5, columns 1–7.
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 8 and 8. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #269.
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: mint spans 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 #269
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Columns 1, 2, 3, 4, 5 and 8 are the tightest columns, with 3 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 7 rows. Row 8 is the crowded extreme at 4 colors — worth revisiting later, not now.
Working through the middle game
The middle of #269 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 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.
Resist the plausible-looking queen. On #269 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 #269 is rated medium
The medium label comes out of four measurable things about #269: two of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 19. Boards that score tight on those measures give up their first queen fast.
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 #269 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 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.
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 #269 is row 1.
A non-spoiling distribution check: solved, #269 carries 3 queens on the perimeter against 5 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 8x8 Queens puzzle #269?
Puzzle #269 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 8x8 puzzle #269 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #269, 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 #269?
Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.