10x10 Queens Puzzle #182
Difficulty: medium. Place 10 queens on this 10x10 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 22-step reasoning is written out below.
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Step-by-step solution for puzzle #182
What follows is a complete solve of puzzle #182, worked the way a person works it rather than the way a computer does. It runs to 22 deductions — 10 queen placements and 12 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, pairing argument on rows, last square in a row, pairing argument on columns.
Show the full walkthrough (17 steps) — contains the solution
Step 1. 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.
Step 2. All of the amber region's remaining squares (2 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 12 squares come off.
Step 3. Only row 1, column 10 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 10, in indigo and in the ring around that square is now dead.
Step 4. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
The board after step 4 — 1 of 10 queens placed. Step 5. Orange cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 10 squares in all.
Step 6. The amber region is down to one open square, at row 2, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 6, the remaining amber squares, and the ring of neighbours around row 2, column 6.
Step 7. Only row 3, column 4 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 4, in blue and in the ring around that square is now dead.
Step 8. Sea green is down to 4 candidates in rows 9 and 10, columns 7–9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about sea green itself.
Step 9. The khaki region has 4 squares left, spread across rows 6, 8, and 9, 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.
The board after step 9 — 3 of 10 queens placed. Step 10. Here is the pairing argument. The orange and sea green regions have no open squares outside rows 9 and 10 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 7 squares come off in one stroke.
Step 11. Pale yellow is down to 5 candidates in rows 7 and 8, columns 1–3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 12. The khaki region has 3 squares left, spread across rows 6 and 8, columns 7 and 8. 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 13. Wherever slate ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
The board after step 13 — 3 of 10 queens placed. Step 14. Row 9 has a single open square left, at column 5 in the orange region. Every row needs a queen, so this one is forced. Row 9 and column 5 are now spoken for, along with the squares touching that queen.
Step 15. Slate, khaki, and sea green are now boxed into columns 7–9 and nothing else. That is 3 colours needing 3 columns, so they fill those columns between them — which locks every remaining colour out and removes 3 squares at once.
Step 16. 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: 7 squares come off.
Step 17. 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 7; pale yellow has one square left, so its queen takes row 7, column 1; mint has one square left, so its queen takes row 4, column 2; slate has one square left, so its queen takes row 5, column 9; red has one square left, so its queen takes row 6, column 3; sea green has one square left, so its queen takes row 10, 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 10, column 8.
The board after step 17 — 10 of 10 queens placed.
That completes the board: 10 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 10x10 Queens puzzle #182
Board #182 of the 10x10 bank carries a medium rating. Its 100 squares are shared between ten colored regions, and the solution places ten queens: one per row, one per column, one per region, none of them side by side or corner to corner.
Like every board on this site, #182 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 #182 are: amber (2 squares), orange (2 squares), indigo (4 squares), sea green (8 squares), khaki (10 squares), blue (11 squares), pale yellow (13 squares), slate (15 squares), mint (17 squares), red (18 squares). An even split would hand every color 10 squares, so the amber region is running 8 squares under that average while the red region is the roomiest area on the grid with 18 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Amber has only 2 places to put its queen; red has 18. The spread between them on this board is 16 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Square count is only half the story — how a color is arranged counts too. Amber is the tidiest shape on #182, packing 100% of its 1×2 bounding box, whereas khaki straggles across its 4×5 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #182 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.
Amber occupies 2 squares within rows 2–2, columns 5–6. It never leaves row 2, so its queen is locked to that row.
Orange: 2 squares across rows 9–10, columns 5–5. It sits wholly inside column 5, so its queen must be in that column.
Indigo covers 4 squares, spanning 2 rows and 3 columns (rows 1–2, columns 8–10).
Sea green occupies 8 squares within rows 9–10, columns 6–10.
Khaki: 10 squares across rows 6–9, columns 4–8.
Blue covers 11 squares, spanning 3 rows and 6 columns (rows 1–3, columns 4–9).
Pale yellow occupies 13 squares within rows 7–10, columns 1–4.
Slate: 15 squares across rows 3–8, columns 7–10.
Mint covers 17 squares, spanning 6 rows and 4 columns (rows 1–6, columns 1–4).
Red occupies 18 squares within rows 3–7, columns 2–8.
Where to start on this board
The most constrained color is where a solve should begin, and on #182 that is amber with 2 squares. It reaches from row 2 to row 2 and from column 5 to column 6 — 1 row by 2 columns. 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 amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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. Indigo, orange and sea green 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 #182
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 4, 5, 8 and 10 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 9 rows. By contrast row 9 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
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.
The whole middle game reduces to two sweeps. Sweep the ten colors looking for one with a single square left; sweep the ten rows and ten columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 10x10 solve from a stalled one.
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 #182 is rated medium
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 3 colors, and a region-size spread of 16. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a medium board from the rest.
If #182 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 10x10
At 10x10 a full re-scan after every move starts to get slow, so work locally instead. Once a queen goes down, check only the regions, rows and columns that placement actually touched — that is where new information appeared. Fall back to a complete sweep only when the local pass turns up nothing, and your solve times will drop noticeably.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #182 the place to look for one is around column 1.
As a sanity check rather than a spoiler: the finished solution to #182 puts 3 queens on the outer border and 7 queens in the interior, 1 of them in an actual 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 10x10 Queens puzzle #182?
Puzzle #182 is rated medium. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #182 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #182, has been verified to have exactly one valid arrangement of ten queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #182?
Start with the amber region — the most constrained color on this board, with 2 squares spanning rows 2–2 and columns 5–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.