10x10 Queens Puzzle #47
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 22-step reasoning is written out below.
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Step-by-step solution for puzzle #47
What follows is a complete solve of puzzle #47, 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: last square in a region, region shadow, region confined to one line, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Only row 1, column 1 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 1, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The amber region is down to one open square, at row 2, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 10, the remaining amber squares, and the ring of neighbours around row 2, column 10.
Step 3. The slate region has 6 squares left, spread across rows 4–8, 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 4. All of the blue region's remaining squares (4 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
Step 5. Red cannot leave row 6 — every one of its open squares (3 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 7 squares in all.
The board after step 5 — 2 of 10 queens placed. Step 6. The orange region has 4 squares left, spread across rows 8–10, 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 7. Wherever sea green ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 8. Here is the pairing argument. The pale yellow, khaki, orange, and sea green regions have no open squares outside rows 7–10 — 4 colours confined to 4 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 2 squares come off in one stroke.
Step 9. The slate region has 3 squares left, spread across rows 4 and 5, 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 10. 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: 2 squares come off.
The board after step 10 — 2 of 10 queens placed. Step 11. Red and sea green are now boxed into columns 4 and 5 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 6 squares at once.
Step 12. 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: 1 square come off.
Step 13. Slate cannot leave row 5 — every one of its open squares (2 open squares) sits there. That row belongs to slate, so every square on it owned by another colour is dead: 4 squares in all.
Step 14. Here is the pairing argument. The blue and slate regions have no open squares outside columns 2 and 3 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 5 squares come off in one stroke.
Step 15. 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: pale yellow has one square left, so its queen takes row 7, column 6; red has one square left, so its queen takes row 6, column 4; slate has one square left, so its queen takes row 5, column 2; blue has one square left, so its queen takes row 3, column 3; orange has one square left, so its queen takes row 9, column 7; sea green has one square left, so its queen takes row 10, column 5; khaki has one square left, so its queen takes row 8, column 9; mint has one square left, so its queen takes row 4, 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 4, column 8.
The board after step 15 — 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 #47
10x10 puzzle #47 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.
Like every board on this site, #47 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 #47 are: indigo (1 square), amber (2 squares), red (3 squares), sea green (3 squares), orange (4 squares), slate (12 squares), khaki (13 squares), blue (15 squares), pale yellow (16 squares), mint (31 squares). An even split would hand every color 10 squares, so the indigo region is running 9 squares under that average while the mint region is the roomiest area on the grid with 31 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Indigo is working with 1 square while mint has 31 to spare, a gap of 30. Attack the cramped end and the roomy regions tend to resolve themselves.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×1 frame; pale yellow is the loosest, occupying only 46% of its 5×7 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Indigo occupies 1 square within rows 1–1, columns 1–1. It never leaves row 1, so its queen is locked to that row.
Amber: 2 squares across rows 1–2, columns 10–10. It sits wholly inside column 10, so its queen must be in that column.
Red covers 3 squares, spanning 1 row and 3 columns (rows 6–6, columns 3–5). It never leaves row 6, so its queen is locked to that row.
Sea green occupies 3 squares within rows 9–10, columns 4–5.
Orange: 4 squares across rows 8–10, columns 6–7.
Slate covers 12 squares, spanning 6 rows and 3 columns (rows 4–9, columns 1–3).
Khaki occupies 13 squares within rows 7–10, columns 7–10.
Blue: 15 squares across rows 1–4, columns 1–5.
Pale yellow covers 16 squares, spanning 5 rows and 7 columns (rows 6–10, columns 1–7).
Mint occupies 31 squares within rows 1–7, columns 4–10.
Where to start on this board
Open on the tightest color. Here that is indigo, confined to 1 square between rows 1 and 1 and columns 1 and 1. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #47.
Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Red, amber 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 #47
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3 and 5 are the narrowest, touched by only 2 colors. Columns 8 and 9 are the tightest columns, with 2 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 9 rows. By contrast row 9 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
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 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.
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 #47 is rated easy
Ratings track how generous the opening is. On #47 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 30-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
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.
If #47 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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 3 on this board.
As a sanity check rather than a spoiler: the finished solution to #47 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 #47?
Puzzle #47 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #47 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #47, 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 #47?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.