12x12 Queens Puzzle #169
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 25-step reasoning is written out below.
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Step-by-step solution for puzzle #169
What follows is a complete solve of puzzle #169, worked the way a person works it rather than the way a computer does. It runs to 25 deductions — 12 queen placements and 13 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 pairing argument on columns.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows, pairing argument on columns, line confined to one region, last square in a row.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Only row 6, column 7 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 7, the rest of the red 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. Slate cannot leave column 12 — every one of its open squares (5 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 5 squares in all.
Step 4. Wherever blue ends up among its 4 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
Step 5. Pale yellow is down to 4 candidates in rows 7–9, columns 9–11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.
The board after step 5 — 1 of 12 queens placed. Step 6. All of the rose region's remaining squares (2 open squares) lie in row 12. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 10 squares come off.
Step 7. Wherever sea green 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. Teal is down to 4 candidates in rows 10 and 11, columns 9–11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about teal itself.
Step 9. Sea green and teal are now boxed into rows 10 and 11 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 9 squares at once.
Step 10. Here is the pairing argument. The blue, pale yellow, and teal regions have no open squares outside columns 9–11 — 3 colours confined to 3 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 9 squares come off in one stroke.
The board after step 10 — 1 of 12 queens placed. Step 11. Orange cannot leave column 8 — every one of its open squares (2 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 4 squares in all.
Step 12. Every open square left in row 2 (4 open squares) belongs to the amber region. Since that row must contain a queen, amber is the colour that supplies it — so amber squares anywhere else on the board are out, 4 squares in all.
Step 13. Pale yellow, khaki, and orange are now boxed into rows 7–9 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 6 squares at once.
Step 14. All of the blue region's remaining squares (3 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
Step 15. From here the board cascades. Keep alternating the region sweep and the line sweep and 11 queens fall out in order without any new idea being needed: slate has one square left, so its queen takes row 5, column 12; blue has one square left, so its queen takes row 3, column 11; row 10 is down to one square, putting a queen on row 10, column 2; rose has one square left, so its queen takes row 12, column 1; mint has one square left, so its queen takes row 4, column 6; indigo has one square left, so its queen takes row 1, column 5; amber has one square left, so its queen takes row 2, column 3; row 7 is down to one square, putting a queen on row 7, column 9; orange has one square left, so its queen takes row 9, column 8; khaki has one square left, so its queen takes row 8, column 4; teal has one square left, so its queen takes row 11, column 10. 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 11, column 10.
The board after step 15 — 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 #169
Puzzle #169 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.
Like every board on this site, #169 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #169 are: red (1 square), rose (2 squares), indigo (3 squares), slate (6 squares), pale yellow (6 squares), sea green (9 squares), teal (10 squares), blue (12 squares), amber (13 squares), orange (21 squares), khaki (23 squares), mint (38 squares). An even split would hand every color 12 squares, so the red region is running 11 squares under that average while the mint region is the roomiest area on the grid with 38 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So red, with 1 square, is under far more pressure than mint with 38. A 37-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×3 frame; blue is the loosest, occupying only 43% of its 7×4 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 covers 1 square, spanning 1 row and 1 column (rows 6–6, columns 7–7). It never leaves row 6, so its queen is locked to that row.
Rose occupies 2 squares within rows 12–12, columns 1–2. It never leaves row 12, so its queen is locked to that row.
Indigo: 3 squares across rows 1–1, columns 5–7. It never leaves row 1, so its queen is locked to that row.
Slate covers 6 squares, spanning 6 rows and 1 column (rows 4–9, columns 12–12). It sits wholly inside column 12, so its queen must be in that column.
Pale yellow occupies 6 squares within rows 7–9, columns 9–11.
Sea green: 9 squares across rows 10–12, columns 1–6.
Teal covers 10 squares, spanning 3 rows and 4 columns (rows 10–12, columns 9–12).
Blue occupies 12 squares within rows 1–7, columns 9–12.
Amber: 13 squares across rows 1–4, columns 1–5.
Orange covers 21 squares, spanning 8 rows and 4 columns (rows 5–12, columns 7–10).
Khaki occupies 23 squares within rows 6–11, columns 1–6.
Mint: 38 squares across rows 1–8, columns 1–11.
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 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 #169.
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 rose 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 #169
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2 and 3 are the narrowest, touched by only 3 colors. Column 8 is the tightest column, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 11 rows. Row 7, meeting 6 colors, is the opposite case — the busiest line on #169 and the last one you should expect to crack.
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 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 #169 is rated easy
Ratings track how generous the opening is. On #169 you get five regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 37-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.
If #169 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #169, start hunting for it near column 8.
Here is a shape check that gives nothing away: when #169 is solved, 3 queens sit on the outer edge of the grid and 9 sit inside it, with 1 queen in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #169?
Puzzle #169 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #169 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #169, 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 #169?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.