8x8 Queens Puzzle #296
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 15-step reasoning is written out below.
Previous puzzle · All 8x8 puzzles · Next puzzle
Step-by-step solution for puzzle #296
What follows is a complete solve of puzzle #296, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 8 queen placements and 7 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, line confined to one region, pairing argument on rows.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Only row 7, column 5 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 5, the rest of the pale yellow 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 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 3. Only row 8, column 7 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 7, in khaki and in the ring around that square is now dead.
The board after step 3 — 2 of 8 queens placed. Step 4. Wherever mint ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 5. Red is down to 6 candidates in rows 3–6, columns 2–4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.
Step 6. All of the mint 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: 3 squares come off.
Step 7. Wherever indigo 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 7 — 2 of 8 queens placed. Step 8. Every open square left in row 6 (2 open squares) belongs to the red region. Since that row must contain a queen, red is the colour that supplies it — so red squares anywhere else on the board are out, 4 squares in all.
Step 9. 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 3 squares at once.
Step 10. 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 3; red has one square left, so its queen takes row 6, column 2; 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 8; mint has one square left, so its queen takes row 4, column 1; slate has one square left, so its queen takes row 5, 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 5, column 6.
The board after step 10 — 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 #296
This is puzzle number 296 in the 8x8 collection, rated medium. The grid holds 64 squares split between eight colored regions, and a finished board carries eight 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 #296, 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 #296 are: pale yellow (1 square), amber (2 squares), mint (3 squares), indigo (7 squares), khaki (8 squares), blue (10 squares), red (16 squares), slate (17 squares). An even split would hand every color 8 squares, so the pale yellow region is running 7 squares under that average while the slate region is the roomiest area on the grid with 17 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Pale yellow is working with 1 square while slate has 17 to spare, a gap of 16. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The amber region is the most compact color here, filling 100% of the 2×1 box that encloses it, while indigo is the most scattered at 58% of its 3×4 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
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.
Pale yellow occupies 1 square within rows 7–7, columns 5–5. It never leaves row 7, so its queen is locked to that row.
Amber: 2 squares across rows 1–2, columns 8–8. It sits wholly inside column 8, so its queen must be in that column.
Mint covers 3 squares, spanning 2 rows and 2 columns (rows 4–5, columns 1–2).
Indigo occupies 7 squares within rows 1–3, columns 1–4.
Khaki: 8 squares across rows 7–8, columns 4–8.
Blue covers 10 squares, spanning 3 rows and 5 columns (rows 1–3, columns 3–7).
Red occupies 16 squares within rows 3–8, columns 1–4.
Slate: 17 squares across rows 3–6, columns 4–8.
Where to start on this board
The most constrained color is where a solve should begin, and on #296 that is pale yellow with 1 square. It reaches from row 7 to row 7 and from column 5 to column 5 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Because pale yellow never leaves row 7, its queen must be in that row — and that instantly settles row 7 for everyone else. Sweep along it and X out every square that is not pale yellow. 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. Amber, mint and khaki 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 #296
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 6 and 8 are the narrowest, touched by only 2 colors. Columns 1, 2, 3, 6, 7 and 8 are the tightest columns, with 3 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 7 rows. Row 3, meeting 4 colors, is the opposite case — the busiest line on #296 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.
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 #296 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 #296 is rated medium
The medium label comes out of four measurable things about #296: three 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 16. 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 #296 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.
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 6 on this board.
Here is a shape check that gives nothing away: when #296 is solved, 4 queens sit on the outer edge of the grid and 4 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 8x8 Queens puzzle #296?
Puzzle #296 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 8x8 puzzle #296 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #296, 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 #296?
Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.