10x10 Queens Puzzle #12
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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #12
What follows is a complete solve of puzzle #12, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 10 queen placements and 5 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 region shadow.
Techniques this board needs: last square in a region, region shadow, region confined to one line.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Only row 6, column 5 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 5, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. The indigo region is down to one open square, at row 1, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 6, the remaining indigo squares, and the ring of neighbours around row 1, column 6.
Step 3. The blue region has 7 squares left, spread across rows 2–4, columns 7–10. 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 3 — 2 of 10 queens placed. Step 4. All of the khaki region's remaining squares (3 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
Step 5. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: sea green has one square left, so its queen takes row 10, column 8; khaki has one square left, so its queen takes row 8, column 7; orange has one square left, so its queen takes row 9, column 4; pale yellow has one square left, so its queen takes row 7, 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 7, column 1.
Step 6. The amber region has 4 squares left, spread across rows 2–4, 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.
The board after step 6 — 6 of 10 queens placed. Step 7. Wherever mint ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. 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 9. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: mint has one square left, so its queen takes row 4, column 2; amber has one square left, so its queen takes row 2, column 3; blue has one square left, so its queen takes row 3, column 10; slate has one square left, so its queen takes row 5, column 9. 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 5, column 9.
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 #12
This is puzzle number 12 in the 10x10 collection, rated easy. The grid holds 100 squares split between ten colored regions, and a finished board carries ten queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
There is exactly one way to finish #12, 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 #12 are: red (1 square), indigo (2 squares), sea green (2 squares), orange (5 squares), pale yellow (11 squares), khaki (11 squares), amber (13 squares), blue (13 squares), mint (15 squares), slate (27 squares). An even split would hand every color 10 squares, so the red region is running 9 squares under that average while the slate region is the roomiest area on the grid with 27 squares.
Every color takes one queen and one only, whatever its size — which is why the 26 square difference between red and slate 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.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×2 frame; slate is the loosest, occupying only 48% of its 8×7 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.
Red: 1 square across rows 6–6, columns 5–5. It never leaves row 6, so its queen is locked to that row.
Indigo covers 2 squares, spanning 1 row and 2 columns (rows 1–1, columns 5–6). It never leaves row 1, so its queen is locked to that row.
Sea green occupies 2 squares within rows 9–10, columns 8–8. It sits wholly inside column 8, so its queen must be in that column.
Orange: 5 squares across rows 7–10, columns 4–5.
Pale yellow covers 11 squares, spanning 4 rows and 4 columns (rows 7–10, columns 1–4).
Khaki occupies 11 squares within rows 6–10, columns 5–7.
Amber: 13 squares across rows 1–4, columns 2–6.
Blue covers 13 squares, spanning 4 rows and 5 columns (rows 1–4, columns 6–10).
Mint occupies 15 squares within rows 1–7, columns 1–4.
Slate: 27 squares across rows 3–10, columns 4–10.
Where to start on this board
Red is the natural opening on #12: it is the smallest region on the grid at 1 square, boxed into rows 6–6 and columns 5–5. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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 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 #12
A quick way to find the next move is to count how many different colors touch each line. On this board, row 5 is the narrowest, touched by only 2 colors. Columns 1, 9 and 10 are the tightest columns, with 2 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 9 rows. Row 10 is the crowded extreme at 5 colors — worth revisiting later, not now.
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.
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.
Resist the plausible-looking queen. On #12 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #12 is rated easy
Ratings track how generous the opening is. On #12 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 26-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 #12 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.
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 #12 is row 5.
A non-spoiling distribution check: solved, #12 carries 4 queens on the perimeter against 6 queens inside, with the corners empty. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.
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 #12?
Puzzle #12 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 #12 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #12, 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 #12?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.