12x12 Queens Puzzle #97
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #97
What follows is a complete solve of puzzle #97, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 12 queen placements and 4 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, last square in a column.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Only row 1, column 12 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 12, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. Blue is down to 4 candidates in rows 2 and 3, columns 1–3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 3. Teal cannot leave row 11 — every one of its open squares (2 open squares) sits there. That row belongs to teal, so every square on it owned by another colour is dead: 13 squares in all.
The board after step 3 — 1 of 12 queens placed. Step 4. The rose region is down to one open square, at row 12, column 9. Every colour holds exactly one queen, so that square is forced. Row 12 and column 9 are now spoken for, along with the squares touching that queen.
Step 5. Only row 11, column 11 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 11, the rest of the teal region and every square adjacent to it — diagonals included.
Step 6. The orange region has 2 squares left, spread across rows 9 and 10, columns 8 and 10. 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. Only row 10, column 7 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 7, in sea green and in the ring around that square is now dead.
The board after step 7 — 4 of 12 queens placed. Step 8. The orange region is down to one open square, at row 9, column 10. Every colour holds exactly one queen, so that square is forced. Row 9 and column 10 are now spoken for, along with the squares touching that queen.
Step 9. Amber cannot leave row 2 — every one of its open squares (3 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 4 squares in all.
Step 10. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 1; red has one square left, so its queen takes row 6, column 2; khaki has one square left, so its queen takes row 8, column 4; column 3 is down to one square, putting a queen on row 4, column 3; slate has one square left, so its queen takes row 5, column 8; pale yellow has one square left, so its queen takes row 7, column 6; amber has one square left, so its queen takes row 2, column 5. 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 2, column 5.
The board after step 10 — 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 #97
Puzzle #97 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 #97, 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 #97 are: indigo (1 square), rose (3 squares), red (5 squares), blue (6 squares), teal (6 squares), sea green (9 squares), orange (12 squares), mint (18 squares), slate (18 squares), pale yellow (19 squares), amber (23 squares), khaki (24 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the khaki region is the roomiest area on the grid with 24 squares.
Every color takes one queen and one only, whatever its size — which is why the 23 square difference between indigo 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. Indigo is the densest region on this grid at 100% of a 1×1 frame; orange is the loosest, occupying only 40% of its 6×5 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 covers 1 square, spanning 1 row and 1 column (rows 1–1, columns 12–12). It never leaves row 1, so its queen is locked to that row.
Rose occupies 3 squares within rows 12–12, columns 9–11. It never leaves row 12, so its queen is locked to that row.
Red: 5 squares across rows 5–8, columns 1–2.
Blue covers 6 squares, spanning 3 rows and 3 columns (rows 1–3, columns 1–3).
Teal occupies 6 squares within rows 9–12, columns 10–12.
Sea green: 9 squares across rows 9–12, columns 5–8.
Orange covers 12 squares, spanning 6 rows and 5 columns (rows 6–11, columns 8–12).
Mint occupies 18 squares within rows 1–6, columns 1–6.
Slate: 18 squares across rows 3–7, columns 6–12.
Pale yellow covers 19 squares, spanning 4 rows and 9 columns (rows 5–8, columns 2–10).
Amber occupies 23 squares within rows 1–4, columns 5–12.
Khaki: 24 squares across rows 8–12, columns 1–6.
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 12 and 12. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #97.
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. Rose is no more than two rows tall, so its queen is 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 #97
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2 and 4 are the narrowest, touched by only 3 colors. Column 4 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 6 is the crowded extreme at 5 colors — worth revisiting later, not now.
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.
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.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #97 is rated medium
Ratings track how generous the opening is. On #97 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 23-square gap between the largest and smallest regions. Those four numbers largely explain the medium 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.
Stuck on #97 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 #97 is row 2.
A non-spoiling distribution check: solved, #97 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 #97?
Puzzle #97 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #97 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #97, 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 #97?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 12–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.