8x8 Queens Puzzle #41
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #41
What follows is a complete solve of puzzle #41, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 8 queen placements and 10 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: region shadow, region confined to one line, last square in a region, line confined to one region, last square in a row, pairing argument on columns.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Wherever amber 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 2. All of the blue region's remaining squares (3 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 3. Only row 8, column 2 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 2, in khaki and in the ring around that square is now dead.
Step 4. The pale yellow region is down to one open square, at row 7, column 8. Every colour holds exactly one queen, so that square is forced. Row 7 and column 8 are now spoken for, along with the squares touching that queen.
Step 5. Indigo is down to 5 candidates in rows 1 and 2, columns 5–7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
The board after step 5 — 2 of 8 queens placed. Step 6. The amber region has 3 squares left, spread across rows 1 and 2, columns 3 and 4. 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. Wherever slate 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.
Step 8. All of the red region's remaining squares (2 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
Step 9. The slate region has 3 squares left, spread across rows 4 and 5, columns 6 and 7. 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.
The board after step 9 — 2 of 8 queens placed. Step 10. Every open square left in row 5 (2 open squares) belongs to the slate region. Since that row must contain a queen, slate is the colour that supplies it — so slate squares anywhere else on the board are out, 1 square in all.
Step 11. Row 4 has only mint squares left (3 open squares). The row needs a queen and only mint can provide one, which pins that colour to this row and kills its squares elsewhere: 5 squares.
Step 12. Row 3 has a single open square left, at column 1 in the blue region. Every row needs a queen, so this one is forced. Cross out the whole of row 3 and column 1, the remaining blue squares, and the ring of neighbours around row 3, column 1.
Step 13. Amber and red are now boxed into columns 3 and 4 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 14. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: mint has one square left, so its queen takes row 4, column 5; slate has one square left, so its queen takes row 5, column 7; indigo has one square left, so its queen takes row 1, column 6; amber has one square left, so its queen takes row 2, column 4; red has one square left, so its queen takes row 6, 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 6, column 3.
The board after step 14 — 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 #41
Puzzle #41 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, #41 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 #41 are: pale yellow (2 squares), blue (3 squares), khaki (3 squares), amber (5 squares), indigo (7 squares), slate (11 squares), red (16 squares), mint (17 squares). An even split would hand every color 8 squares, so the pale yellow region is running 6 squares under that average while the mint region is the roomiest area on the grid with 17 squares.
Every color takes one queen and one only, whatever its size — which is why the 15 square difference between pale yellow and mint 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.
Square count is only half the story — how a color is arranged counts too. Blue is the tidiest shape on #41, packing 100% of its 3×1 bounding box, whereas mint straggles across its 5×7 box at just 49%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #41 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.
Pale yellow occupies 2 squares within rows 7–8, columns 8–8. It sits wholly inside column 8, so its queen must be in that column.
Blue: 3 squares across rows 1–3, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Khaki covers 3 squares, spanning 2 rows and 2 columns (rows 7–8, columns 1–2).
Amber occupies 5 squares within rows 1–2, columns 2–4.
Indigo: 7 squares across rows 1–2, columns 5–8.
Slate covers 11 squares, spanning 5 rows and 3 columns (rows 4–8, columns 6–8).
Red occupies 16 squares within rows 4–8, columns 1–6.
Mint: 17 squares across rows 2–6, columns 2–8.
Where to start on this board
Open on the tightest color. Here that is pale yellow, confined to 2 squares between rows 7 and 8 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 #41.
Because pale yellow 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. Amber, indigo 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 #41
A quick way to find the next move is to count how many different colors touch each line. On this board, row 3 is the narrowest, touched by only 2 colors. Columns 1, 3, 4, 5 and 7 are the tightest columns, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 7 rows. By contrast row 8 meets 4 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
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 #41 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 2-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 15. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
If #41 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.
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 #41 is row 3.
As a sanity check rather than a spoiler: the finished solution to #41 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 #41?
Puzzle #41 is rated hard. Its smallest color region holds 2 squares, 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 #41 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #41, 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 #41?
Start with the pale yellow region — the most constrained color on this board, with 2 squares spanning rows 7–8 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.