10x10 Queens Puzzle #183
Difficulty: easy. 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 20-step reasoning is written out below.
Previous puzzle · All 10x10 puzzles · Next puzzle
Step-by-step solution for puzzle #183
What follows is a complete solve of puzzle #183, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 10 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: last square in a region, region confined to one line, region shadow, pairing argument on rows, pairing argument on columns, last square in a row.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Only row 5, column 7 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 7, the rest of the slate region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 9 squares come off.
Step 3. The blue region has 4 squares left, spread across rows 1–3, columns 2–4. 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 4. Wherever khaki ends up among its 3 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
The board after step 4 — 1 of 10 queens placed. Step 5. Sea green cannot leave row 10 — every one of its open squares (2 open squares) sits there. That row belongs to sea green, so every square on it owned by another colour is dead: 6 squares in all.
Step 6. The khaki region has 2 squares left, spread across rows 8 and 9, columns 2 and 3. 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, amber, and blue are now boxed into rows 1–3 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 8. Here is the pairing argument. The pale yellow, khaki, and orange regions have no open squares outside rows 7–9 — 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.
The board after step 8 — 1 of 10 queens placed. Step 9. Blue, khaki, and sea green are now boxed into columns 2–4 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 10 squares at once.
Step 10. All of the red region's remaining squares (2 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 11. Orange cannot leave column 6 — 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: 4 squares in all.
Step 12. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: row 3 is down to one square, putting a queen on row 3, column 2; indigo has one square left, so its queen takes row 1, column 1; amber has one square left, so its queen takes row 2, column 8; khaki has one square left, so its queen takes row 8, column 3; orange has one square left, so its queen takes row 9, column 6; pale yellow has one square left, so its queen takes row 7, column 10; mint has one square left, so its queen takes row 4, column 9; red has one square left, so its queen takes row 6, column 5; sea green has one square left, so its queen takes row 10, column 4. 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 4.
The board after step 12 — 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 #183
10x10 puzzle #183 is rated easy. Ten colored regions cover its 100 squares, and your job is to seat ten queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Puzzle #183 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #183 are: slate (1 square), indigo (2 squares), sea green (4 squares), blue (8 squares), khaki (8 squares), orange (10 squares), amber (13 squares), pale yellow (15 squares), mint (16 squares), red (23 squares). An even split would hand every color 10 squares, so the slate region is running 9 squares under that average while the red region is the roomiest area on the grid with 23 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Slate has only 1 place to put its queen; red has 23. The spread between them on this board is 22 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 2×1 frame; orange is the loosest, occupying only 50% of its 4×5 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 easy board.
Slate: 1 square across rows 5–5, columns 7–7. It never leaves row 5, so its queen is locked to that row.
Indigo covers 2 squares, spanning 2 rows and 1 column (rows 1–2, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Sea green occupies 4 squares within rows 10–10, columns 1–4. It never leaves row 10, so its queen is locked to that row.
Blue: 8 squares across rows 1–4, columns 1–4.
Khaki covers 8 squares, spanning 5 rows and 3 columns (rows 5–9, columns 1–3).
Orange occupies 10 squares within rows 7–10, columns 3–7.
Amber: 13 squares across rows 1–3, columns 4–10.
Pale yellow covers 15 squares, spanning 4 rows and 5 columns (rows 7–10, columns 6–10).
Mint occupies 16 squares within rows 2–7, columns 7–10.
Red: 23 squares across rows 3–8, columns 2–7.
Where to start on this board
Open on the tightest color. Here that is slate, confined to 1 square between rows 5 and 5 and columns 7 and 7. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #183.
Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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. Sea green and indigo 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 #183
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 4, 6, 9 and 10 are the narrowest, touched by only 3 colors. Columns 5, 8, 9 and 10 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 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 7 meets 5 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 ten 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 10x10 board unwinds.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #183 is rated easy
The easy label comes out of four measurable things about #183: four of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 22. 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.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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 #183 the place to look for one is around row 1.
As a sanity check rather than a spoiler: the finished solution to #183 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 10x10 Queens puzzle #183?
Puzzle #183 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #183 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #183, 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 #183?
Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.