12x12 Queens Puzzle #160
Difficulty: hard. 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 17-step reasoning is written out below.
Previous puzzle · All 12x12 puzzles · Next puzzle
Step-by-step solution for puzzle #160
What follows is a complete solve of puzzle #160, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 12 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 pairing argument on rows.
Techniques this board needs: last square in a region, pairing argument on rows, region shadow, region confined to one line.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 7, column 4 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 4, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 2. Here is the pairing argument. The indigo, amber, blue, and mint regions have no open squares outside rows 1–4 — 4 colours confined to 4 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 10 squares come off in one stroke.
Step 3. Only row 5, column 11 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 11, in slate and in the ring around that square is now dead.
Step 4. Wherever indigo ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
The board after step 4 — 2 of 12 queens placed. Step 5. Blue cannot leave column 12 — every one of its open squares (3 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 5 squares in all.
Step 6. The khaki region is down to one open square, at row 8, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 10, the remaining khaki squares, and the ring of neighbours around row 8, column 10.
Step 7. Only row 1, column 9 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 9, in indigo and in the ring around that square is now dead.
The board after step 7 — 4 of 12 queens placed. Step 8. The red region is down to one open square, at row 6, column 1. Every colour holds exactly one queen, so that square is forced. Row 6 and column 1 are now spoken for, along with the squares touching that queen.
Step 9. 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.
Step 10. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 11. 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: sea green has one square left, so its queen takes row 10, 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 12; mint has one square left, so its queen takes row 4, column 6; orange has one square left, so its queen takes row 9, column 7; teal has one square left, so its queen takes row 11, column 5; rose has one square left, so its queen takes row 12, 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 12, column 8.
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 #160
This is puzzle number 160 in the 12x12 collection, rated hard. The grid holds 144 squares split between twelve colored regions, and a finished board carries twelve queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
Puzzle #160 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #160 are: pale yellow (1 square), indigo (5 squares), blue (5 squares), slate (8 squares), amber (10 squares), sea green (10 squares), red (11 squares), teal (13 squares), rose (15 squares), mint (18 squares), khaki (20 squares), orange (28 squares). An even split would hand every color 12 squares, so the pale yellow region is running 11 squares under that average while the orange region is the roomiest area on the grid with 28 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Pale yellow is working with 1 square while orange has 28 to spare, a gap of 27. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The pale yellow region is the most compact color here, filling 100% of the 1×1 box that encloses it, while sea green is the most scattered at 50% of its 5×4 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
Region by region
Below is every color on #160 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Pale yellow covers 1 square, spanning 1 row and 1 column (rows 7–7, columns 4–4). It never leaves row 7, so its queen is locked to that row.
Indigo occupies 5 squares within rows 1–3, columns 9–11.
Blue: 5 squares across rows 1–3, columns 11–12.
Slate covers 8 squares, spanning 3 rows and 5 columns (rows 3–5, columns 8–12).
Amber occupies 10 squares within rows 1–4, columns 1–4.
Sea green: 10 squares across rows 8–12, columns 1–4.
Red covers 11 squares, spanning 5 rows and 3 columns (rows 4–8, columns 1–3).
Teal occupies 13 squares within rows 8–12, columns 2–6.
Rose: 15 squares across rows 9–12, columns 5–10.
Mint covers 18 squares, spanning 4 rows and 7 columns (rows 1–4, columns 3–9).
Khaki occupies 20 squares within rows 5–12, columns 9–12.
Orange: 28 squares across rows 4–10, columns 2–9.
Where to start on this board
The most constrained color is where a solve should begin, and on #160 that is pale yellow with 1 square. It reaches from row 7 to row 7 and from column 4 to column 4 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Because pale yellow never leaves row 7, its queen must be in that row — and that instantly settles row 7 for everyone else. Sweep along it and X out every square that is not pale yellow. 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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: blue spans only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.
The tightest lines on puzzle #160
A quick way to find the next move is to count how many different colors touch each line. On this board, row 6 is the narrowest, touched by only 3 colors. Columns 1, 7 and 12 are the tightest columns, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 11 rows. By contrast row 10 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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 #160 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 27. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 6 on this board.
As a sanity check rather than a spoiler: the finished solution to #160 puts 4 queens on the outer border and 8 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 12x12 Queens puzzle #160?
Puzzle #160 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #160 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #160, 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 #160?
Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.