8x8 Queens Puzzle #165
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #165
What follows is a complete solve of puzzle #165, 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 rows.
Techniques this board needs: region shadow, region confined to one line, pairing argument on rows, last square in a region.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Wherever indigo ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 2. All of the slate region's remaining squares (3 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 3. The amber region has 3 squares left, spread across rows 1 and 2, columns 6 and 7. 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. Wherever khaki 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 4 — 0 of 8 queens placed. Step 5. Amber is down to 2 candidates in rows 1 and 2, columns 6 and 7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 6. The mint region has 6 squares left, spread across rows 1–5, columns 4 and 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 7. 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 8. Mint is down to 4 candidates in rows 3–5, columns 4 and 5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
The board after step 8 — 0 of 8 queens placed. Step 9. Blue, mint, and slate are now boxed into rows 3–5 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 7 squares at once.
Step 10. Wherever red ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 11. Khaki cannot leave column 7 — every one of its open squares (2 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 3 squares in all.
Step 12. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: amber has one square left, so its queen takes row 2, column 6; indigo has one square left, so its queen takes row 1, column 2; red has one square left, so its queen takes row 6, column 5; mint has one square left, so its queen takes row 4, column 4; blue has one square left, so its queen takes row 3, column 1; slate has one square left, so its queen takes row 5, column 8; khaki has one square left, so its queen takes row 8, column 7; pale yellow has one square left, so its queen takes row 7, 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 7, column 3.
The board after step 12 — 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 #165
Puzzle #165 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.
Like every board on this site, #165 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #165 are: slate (3 squares), indigo (4 squares), amber (5 squares), red (8 squares), blue (9 squares), mint (9 squares), khaki (9 squares), pale yellow (17 squares). An even split would hand every color 8 squares, so the slate region is running 5 squares under that average while the pale yellow region is the roomiest area on the grid with 17 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 slate, with 3 squares, is under far more pressure than pale yellow with 17. 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. Slate is the tidiest shape on #165, packing 100% of its 3×1 bounding box, whereas mint straggles across its 5×4 box at just 45%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #165 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Slate: 3 squares across rows 3–5, columns 8–8. It sits wholly inside column 8, so its queen must be in that column.
Indigo covers 4 squares, spanning 2 rows and 3 columns (rows 1–2, columns 2–4).
Amber occupies 5 squares within rows 1–2, columns 6–8.
Red: 8 squares across rows 4–8, columns 5–7.
Blue covers 9 squares, spanning 5 rows and 4 columns (rows 1–5, columns 1–4).
Mint occupies 9 squares within rows 1–5, columns 3–6.
Khaki: 9 squares across rows 3–8, columns 6–8.
Pale yellow covers 17 squares, spanning 5 rows and 5 columns (rows 4–8, columns 1–5).
Where to start on this board
Open on the tightest color. Here that is slate, confined to 3 squares between rows 3 and 5 and columns 8 and 8. Its queen has nowhere else to go, which means those 3 rows and 1 column carry more constraint than anywhere else on #165.
Because slate 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. Indigo and amber 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 #165
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 6, 7 and 8 are the narrowest, touched by only 3 colors. Column 1 is the tightest column, with 2 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 7 rows. By contrast row 5 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
With eight queens to seat and eight regions competing over 64 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 8x8 boards quickly and players who stall halfway.
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 #165 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers one single-line region, a 3-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 14. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
If #165 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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 #165, start hunting for it near column 1.
As a sanity check rather than a spoiler: the finished solution to #165 puts 4 queens on the outer border and 4 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 #165?
Puzzle #165 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 8x8 puzzle #165 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #165, 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 #165?
Start with the slate region — the most constrained color on this board, with 3 squares spanning rows 3–5 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.