10x10 Queens Puzzle #27
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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #27
What follows is a complete solve of puzzle #27, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 10 queen placements and 7 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 line confined to one region.
Techniques this board needs: region confined to one line, last square in a region, region shadow, line confined to one region, last square in a row.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 8 squares in all.
Step 2. The amber region is down to one open square, at row 2, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 2, the remaining amber squares, and the ring of neighbours around row 2, column 2.
Step 3. Red cannot leave column 1 — every one of its open squares (3 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 4 squares in all.
The board after step 3 — 1 of 10 queens placed. Step 4. All of the khaki region's remaining squares (2 open squares) lie in column 10. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 8 squares come off.
Step 5. Orange is down to 5 candidates in rows 8–10, columns 4 and 5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about orange itself.
Step 6. All of the sea green region's remaining squares (2 open squares) lie in row 10. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
The board after step 6 — 1 of 10 queens placed. Step 7. Wherever orange 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. Every open square left in row 3 (6 open squares) belongs to the blue region. Since that row must contain a queen, blue is the colour that supplies it — so blue squares anywhere else on the board are out, 9 squares in all.
Step 9. 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 4 is down to one square, putting a queen on row 4, column 3; row 5 is down to one square, putting a queen on row 5, column 8; sea green has one square left, so its queen takes row 10, column 9; khaki has one square left, so its queen takes row 8, column 10; orange has one square left, so its queen takes row 9, column 5; indigo has one square left, so its queen takes row 1, column 4; pale yellow has one square left, so its queen takes row 7, column 6; blue has one square left, so its queen takes row 3, column 7; red has one square left, so its queen takes row 6, column 1. 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 1.
The board after step 9 — 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 #27
10x10 puzzle #27 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.
There is exactly one way to finish #27, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these ten regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #27 are: khaki (2 squares), indigo (3 squares), amber (3 squares), sea green (3 squares), orange (5 squares), red (6 squares), pale yellow (11 squares), slate (14 squares), mint (24 squares), blue (29 squares). An even split would hand every color 10 squares, so the khaki region is running 8 squares under that average while the blue region is the roomiest area on the grid with 29 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Khaki is working with 2 squares while blue has 29 to spare, a gap of 27. Attack the cramped end and the roomy regions tend to resolve themselves.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #27, packing 100% of its 1×3 bounding box, whereas mint straggles across its 9×5 box at just 53%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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.
Khaki: 2 squares across rows 8–9, columns 10–10. It sits wholly inside column 10, so its queen must be in that column.
Indigo covers 3 squares, spanning 1 row and 3 columns (rows 1–1, columns 3–5). It never leaves row 1, so its queen is locked to that row.
Amber occupies 3 squares within rows 1–2, columns 1–2.
Sea green: 3 squares across rows 10–10, columns 8–10. It never leaves row 10, so its queen is locked to that row.
Orange covers 5 squares, spanning 3 rows and 2 columns (rows 8–10, columns 4–5).
Red occupies 6 squares within rows 6–8, columns 1–2.
Pale yellow: 11 squares across rows 6–10, columns 4–7.
Slate covers 14 squares, spanning 5 rows and 5 columns (rows 5–9, columns 6–10).
Mint occupies 24 squares within rows 2–10, columns 1–5.
Blue: 29 squares across rows 1–5, columns 4–10.
Where to start on this board
Open on the tightest color. Here that is khaki, confined to 2 squares between rows 8 and 9 and columns 10 and 10. Its queen has nowhere else to go, which means those 2 rows and 1 column carry more constraint than anywhere else on #27.
Because khaki stays inside column 10, its queen belongs to that column and no other region may use it. Cross out the rest of column 10 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, sea green 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 #27
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3 and 4 are the narrowest, touched by only 2 colors. Column 3 is the tightest column, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 9 rows. Row 8 sits at the far end with 6 colors crossing it; it will almost certainly be among the last to settle.
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.
Two checks, run alternately, will carry you through the 100 squares of this grid. First: has any of the ten regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 10x10 boards almost always run one of those checks and forget the other.
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 #27 is rated easy
Ratings track how generous the opening is. On #27 you get three regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 27-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
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 easy board from the rest.
Stuck on #27 despite the easy rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 6 queens in the middle, and nothing in the corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #27?
Puzzle #27 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #27 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #27, 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 #27?
Start with the khaki region — the most constrained color on this board, with 2 squares spanning rows 8–9 and columns 10–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.