12x12 Queens Puzzle #225
Difficulty: medium. 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 14-step reasoning is written out below.
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Step-by-step solution for puzzle #225
What follows is a complete solve of puzzle #225, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 12 queen placements and 2 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 (8 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: red has one square left, so its queen takes row 6, column 5; rose has one square left, so its queen takes row 12, column 1; teal has one square left, so its queen takes row 11, column 3; sea green has one square left, so its queen takes row 10, column 12; pale yellow has one square left, so its queen takes row 7, column 11; amber has one square left, so its queen takes row 2, column 10; slate has one square left, so its queen takes row 5, column 2. 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 2.
Step 2. All of the indigo region's remaining squares (3 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 3. Only row 3, column 4 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 4, the rest of the blue region and every square adjacent to it — diagonals included.
Step 4. The mint region is down to one open square, at row 4, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 6, the remaining mint squares, and the ring of neighbours around row 4, column 6.
The board after step 4 — 9 of 12 queens placed. Step 5. Khaki is down to 4 candidates in rows 8 and 9, columns 7–9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about khaki itself.
Step 6. The orange region is down to one open square, at row 9, column 9. Every colour holds exactly one queen, so that square is forced. Row 9 and column 9 are now spoken for, along with the squares touching that queen.
Step 7. Only row 8, column 7 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 7, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 8. The indigo region is down to one open square, at row 1, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 8, the remaining indigo squares, and the ring of neighbours around row 1, column 8.
The board after step 8 — 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 #225
Puzzle #225 is one of the medium-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.
There is exactly one way to finish #225, 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 twelve regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #225 are: red (1 square), rose (1 square), sea green (3 squares), amber (4 squares), pale yellow (9 squares), teal (9 squares), slate (12 squares), mint (15 squares), blue (16 squares), orange (16 squares), indigo (18 squares), khaki (40 squares). An even split would hand every color 12 squares, so the red region is running 11 squares under that average while the khaki region is the roomiest area on the grid with 40 squares.
Every color takes one queen and one only, whatever its size — which is why the 39 square difference between red and khaki 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. Red is the densest region on this grid at 100% of a 1×1 frame; indigo is the loosest, occupying only 43% of its 6×7 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 medium board.
Red: 1 square across rows 6–6, columns 5–5. It never leaves row 6, so its queen is locked to that row.
Rose covers 1 square, spanning 1 row and 1 column (rows 12–12, columns 1–1). It never leaves row 12, so its queen is locked to that row.
Sea green occupies 3 squares within rows 10–12, columns 12–12. It sits wholly inside column 12, so its queen must be in that column.
Amber: 4 squares across rows 2–3, columns 10–12.
Pale yellow covers 9 squares, spanning 6 rows and 3 columns (rows 4–9, columns 10–12).
Teal occupies 9 squares within rows 10–12, columns 2–6.
Slate: 12 squares across rows 3–11, columns 1–2.
Mint covers 15 squares, spanning 5 rows and 5 columns (rows 3–7, columns 3–7).
Blue occupies 16 squares within rows 1–4, columns 1–7.
Orange: 16 squares across rows 7–12, columns 8–11.
Indigo covers 18 squares, spanning 6 rows and 7 columns (rows 1–6, columns 6–12).
Khaki occupies 40 squares within rows 3–12, columns 2–9.
Where to start on this board
Open on the tightest color. Here that is red, confined to 1 square between rows 6 and 6 and columns 5 and 5. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #225.
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. Rose 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 #225
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Columns 1, 8 and 9 are the tightest columns, with 3 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 11 rows. Row 6 is the crowded extreme at 6 colors — worth revisiting later, not now.
Working through the middle game
The middle of #225 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
Two checks, run alternately, will carry you through the 144 squares of this grid. First: has any of the twelve regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 12x12 boards almost always run one of those checks and forget the other.
Resist the plausible-looking queen. On #225 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 #225 is rated medium
The medium label comes out of four measurable things about #225: five of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 39. Boards that score tight on those measures give up their first queen fast.
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.
Stuck on #225 despite the medium 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 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 #225 is row 1.
A non-spoiling distribution check: solved, #225 carries 3 queens on the perimeter against 9 queens inside, 1 of them cornered. 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 #225?
Puzzle #225 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #225 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #225, 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 #225?
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.