12x12 Queens Puzzle #5
Difficulty: easy. Place 12 queens on this 12x12 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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #5
What follows is a complete solve of puzzle #5, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 12 queen placements and 6 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 confined to one line, region shadow.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 12, column 7 is still open in rose, and since each colour must take a queen, that settles it. That clears row 12, column 7, the rest of the rose region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 11 squares come off.
Step 3. 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: 12 squares in all.
Step 4. All of the teal region's remaining squares (2 open squares) lie in row 11. 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 4 — 1 of 12 queens placed. Step 5. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: orange has one square left, so its queen takes row 9, column 3; khaki has one square left, so its queen takes row 8, column 12; indigo has one square left, so its queen takes row 1, column 11; teal has one square left, so its queen takes row 11, column 10; 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.
Step 6. All of the slate region's remaining squares (4 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
Step 7. Only row 2, column 6 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 6, in amber and in the ring around that square is now dead.
The board after step 7 — 7 of 12 queens placed. Step 8. The red region has 5 squares left, spread across rows 5–7, columns 4 and 5. 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 9. Only row 7, column 2 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 2, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 10. All of the mint region's remaining squares (2 open squares) lie in row 4. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 11. 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: red has one square left, so its queen takes row 6, column 5; mint has one square left, so its queen takes row 4, column 4; slate has one square left, so its queen takes row 5, column 9; blue has one square left, so its queen takes row 3, 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 3, column 1.
The board after step 11 — 12 of 12 queens placed.
That completes the board: 12 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 12x12 Queens puzzle #5
Puzzle #5 is one of the easy-rated boards in the 12x12 set. Twelve colors divide its 144 squares, and you win by placing twelve queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
As with every puzzle in this collection, #5 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #5 are: rose (1 square), indigo (2 squares), sea green (2 squares), mint (8 squares), pale yellow (8 squares), teal (9 squares), khaki (10 squares), amber (14 squares), orange (17 squares), blue (18 squares), red (23 squares), slate (32 squares). An even split would hand every color 12 squares, so the rose region is running 11 squares under that average while the slate region is the roomiest area on the grid with 32 squares.
Every color takes one queen and one only, whatever its size — which is why the 31 square difference between rose 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.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #5, packing 100% of its 1×2 bounding box, whereas mint straggles across its 4×5 box at just 40%. 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.
Rose occupies 1 square within rows 12–12, columns 7–7. It never leaves row 12, so its queen is locked to that row.
Indigo: 2 squares across rows 1–1, columns 11–12. It never leaves row 1, so its queen is locked to that row.
Sea green covers 2 squares, spanning 1 row and 2 columns (rows 10–10, columns 8–9). It never leaves row 10, so its queen is locked to that row.
Mint occupies 8 squares within rows 4–7, columns 1–5.
Pale yellow: 8 squares across rows 6–9, columns 1–4.
Teal covers 9 squares, spanning 2 rows and 5 columns (rows 11–12, columns 7–11).
Khaki occupies 10 squares within rows 8–12, columns 9–12.
Amber: 14 squares across rows 1–4, columns 5–10.
Orange covers 17 squares, spanning 4 rows and 6 columns (rows 9–12, columns 1–6).
Blue occupies 18 squares within rows 1–5, columns 1–6.
Red: 23 squares across rows 4–10, columns 3–7.
Slate covers 32 squares, spanning 8 rows and 6 columns (rows 2–9, columns 7–12).
Where to start on this board
Open on the tightest color. Here that is rose, confined to 1 square between rows 12 and 12 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 #5.
Because rose never leaves row 12, its queen must be in that row — and that instantly settles row 12 for everyone else. Sweep along it and X out every square that is not rose. 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, sea green and teal 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 #5
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3 and 11 are the narrowest, touched by only 3 colors. Column 12 is the tightest column, with 3 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 11 rows. Row 9 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.
The whole middle game reduces to two sweeps. Sweep the twelve colors looking for one with a single square left; sweep the twelve rows and twelve columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 12x12 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 #5 is rated easy
Ratings track how generous the opening is. On #5 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 31-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
Techniques that work well at 12x12
At 12x12 you are managing 144 squares, and holding the whole board in your head will not work. Split it into quadrants and solve locally. Most useful deductions on a grid this large are regional — a color pinched between two placed queens, or a band of rows that two regions must share. Trust the marks on the board over your memory.
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 #5 is row 1.
A non-spoiling distribution check: solved, #5 carries 4 queens on the perimeter against 8 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 12x12 Queens puzzle #5?
Puzzle #5 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 12x12 puzzle #5 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #5, has been verified to have exactly one valid arrangement of twelve queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #5?
Start with the rose region — the most constrained color on this board, with 1 square spanning rows 12–12 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.