8x8 Queens Puzzle #234
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 13-step reasoning is written out below.
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Step-by-step solution for puzzle #234
What follows is a complete solve of puzzle #234, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 8 queen placements and 5 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, region confined to one line, pairing argument on rows, pairing argument on columns, last square in a row.
Show the full walkthrough (8 steps) — contains the solution
Step 1. Only row 6, column 6 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 6, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. Indigo is down to 4 candidates in rows 1–3, columns 4 and 5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
Step 3. The mint region has 4 squares left, spread across rows 3, 4, 5, and 7, columns 7 and 8. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 4. All of the khaki region's remaining squares (3 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
The board after step 4 — 1 of 8 queens placed. Step 5. Only row 7, column 1 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 1, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 6. Here is the pairing argument. The indigo, amber, and blue regions have no open squares outside rows 1–3 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 3 squares come off in one stroke.
Step 7. Amber and mint are now boxed into columns 7 and 8 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 2 squares at once.
Step 8. 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: khaki has one square left, so its queen takes row 8, column 5; indigo has one square left, so its queen takes row 1, column 4; row 3 is down to one square, putting a queen on row 3, column 2; slate has one square left, so its queen takes row 5, column 3; mint has one square left, so its queen takes row 4, column 7; amber has one square left, so its queen takes row 2, column 8. 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 2, column 8.
The board after step 8 — 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 #234
Board #234 of the 8x8 bank carries a hard rating. Its 64 squares are shared between eight colored regions, and the solution places eight queens: one per row, one per column, one per region, none of them side by side or corner to corner.
As with every puzzle in this collection, #234 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 #234 are: red (1 square), indigo (4 squares), amber (8 squares), blue (8 squares), pale yellow (8 squares), mint (9 squares), khaki (10 squares), slate (16 squares). An even split would hand every color 8 squares, so the red region is running 7 squares under that average while the slate 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 red, with 1 square, is under far more pressure than slate with 16. A 15-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Red is the densest region on this grid at 100% of a 1×1 frame; mint is the loosest, occupying only 60% of its 5×3 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 hard board.
Red: 1 square across rows 6–6, columns 6–6. It never leaves row 6, so its queen is locked to that row.
Indigo covers 4 squares, spanning 3 rows and 2 columns (rows 1–3, columns 4–5).
Amber occupies 8 squares within rows 1–4, columns 6–8.
Blue: 8 squares across rows 1–3, columns 1–4.
Pale yellow covers 8 squares, spanning 3 rows and 4 columns (rows 6–8, columns 1–4).
Mint occupies 9 squares within rows 3–7, columns 6–8.
Khaki: 10 squares across rows 5–8, columns 5–8.
Slate covers 16 squares, spanning 5 rows and 5 columns (rows 3–7, columns 1–5).
Where to start on this board
Red is the natural opening on #234: it is the smallest region on the grid at 1 square, boxed into rows 6–6 and columns 6–6. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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: indigo 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 #234
A quick way to find the next move is to count how many different colors touch each line. On this board, row 8 is the narrowest, touched by only 2 colors. Columns 1, 2, 3, 5, 7 and 8 are the tightest columns, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 7 rows. Row 6 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
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.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #234 is rated hard
The hard label comes out of four measurable things about #234: 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 15. Boards that score tight on those measures give up their first queen fast.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
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 #234, start hunting for it near row 8.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 4 queens in the middle, and nothing in the corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #234?
Puzzle #234 is rated hard. 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 #234 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #234, 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 #234?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.