8x8 Queens Puzzle #245
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 11-step reasoning is written out below.
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Step-by-step solution for puzzle #245
What follows is a complete solve of puzzle #245, worked the way a person works it rather than the way a computer does. It runs to 11 deductions — 8 queen placements and 3 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 region confined to one line.
Techniques this board needs: region confined to one line, last square in a region.
Show the full walkthrough (6 steps) — contains the solution
Step 1. Mint cannot leave column 8 — 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: 8 squares in all.
Step 2. The khaki region is down to one open square, at row 8, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 7, the remaining khaki squares, and the ring of neighbours around row 8, column 7.
Step 3. Only row 2, column 6 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 6, in amber and in the ring around that square is now dead.
The board after step 3 — 2 of 8 queens placed. Step 4. 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: 2 squares come off.
Step 5. Blue cannot leave column 1 — 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: 5 squares in all.
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: pale yellow has one square left, so its queen takes row 7, column 3; indigo has one square left, so its queen takes row 1, column 4; slate has one square left, so its queen takes row 5, column 2; blue has one square left, so its queen takes row 3, column 1; mint has one square left, so its queen takes row 4, column 8; red has one square left, so its queen takes row 6, 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 6, column 5.
The board after step 6 — 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 #245
Puzzle #245 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.
As with every puzzle in this collection, #245 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #245 are: mint (2 squares), khaki (4 squares), blue (6 squares), pale yellow (6 squares), amber (7 squares), indigo (9 squares), slate (14 squares), red (16 squares). An even split would hand every color 8 squares, so the mint region is running 6 squares under that average while the red region is the roomiest area on the grid with 16 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 mint, with 2 squares, is under far more pressure than red with 16. A 14-square gap like this one rewards players who start where the choices are fewest.
Square count is only half the story — how a color is arranged counts too. Mint is the tidiest shape on #245, packing 100% of its 2×1 bounding box, whereas red straggles across its 5×6 box at just 53%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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 2 squares within rows 3–4, columns 8–8. It sits wholly inside column 8, so its queen must be in that column.
Khaki: 4 squares across rows 6–8, columns 7–8.
Blue covers 6 squares, spanning 4 rows and 2 columns (rows 1–4, columns 1–2).
Pale yellow occupies 6 squares within rows 7–8, columns 1–4.
Amber: 7 squares across rows 1–4, columns 6–8.
Indigo covers 9 squares, spanning 3 rows and 4 columns (rows 1–3, columns 3–6).
Slate occupies 14 squares within rows 3–7, columns 1–4.
Red: 16 squares across rows 4–8, columns 3–8.
Where to start on this board
Open on the tightest color. Here that is mint, confined to 2 squares between rows 3 and 4 and columns 8 and 8. Its queen has nowhere else to go, which means those 2 rows and 1 column carry more constraint than anywhere else on #245.
Because mint stays inside column 8, its queen belongs to that column and no other region may use it. Cross out the rest of column 8 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 #245
A quick way to find the next move is to count how many different colors touch each line. On this board, row 5 is the narrowest, touched by only 2 colors. Column 5 is the tightest column, 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 7 rows. Row 4 is the crowded extreme at 5 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.
Keep alternating between two views of the board. In the region view you ask which of the eight colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 8x8 board unwinds.
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 #245 is rated hard
Ratings track how generous the opening is. On #245 you get one region pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 14-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.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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 #245, start hunting for it near row 5.
A non-spoiling distribution check: solved, #245 carries 4 queens on the perimeter against 4 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 8x8 Queens puzzle #245?
Puzzle #245 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 8x8 puzzle #245 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #245, 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 #245?
Start with the mint region — the most constrained color on this board, with 2 squares spanning rows 3–4 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.