12x12 Queens Puzzle #120
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 22-step reasoning is written out below.
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Step-by-step solution for puzzle #120
What follows is a complete solve of puzzle #120, worked the way a person works it rather than the way a computer does. It runs to 22 deductions — 12 queen placements and 10 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, region confined to one line, region shadow, pairing argument on rows, last square in a row, line confined to one region, last square in a column.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 2, column 3 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 3, the rest of the amber region and every square adjacent to it — diagonals included.
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: 6 squares come off.
Step 3. Only row 3, column 8 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 8, in blue and in the ring around that square is now dead.
Step 4. 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: 8 squares come off.
Step 5. Slate is down to 3 candidates in rows 5 and 6, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
The board after step 5 — 2 of 12 queens placed. Step 6. The teal region has 3 squares left, spread across rows 11 and 12, columns 1 and 2. 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 7. Wherever rose 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.
Step 8. Here is the pairing argument. The teal and rose regions have no open squares outside rows 11 and 12 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 11 squares come off in one stroke.
Step 9. The orange region has 3 squares left, spread across rows 9 and 10, columns 11 and 12. 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.
The board after step 9 — 2 of 12 queens placed. Step 10. All of the sea green region's remaining squares (2 open squares) lie in row 10. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 10 squares come off.
Step 11. 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 12; mint has one square left, so its queen takes row 4, column 11; indigo has one square left, so its queen takes row 1, column 10; row 11 is down to one square, putting a queen on row 11, column 1; 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 12. Wherever khaki 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.
Step 13. Column 5 has only khaki squares left (3 open squares). The column needs a queen and only khaki can provide one, which pins that colour to this column and kills its squares elsewhere: 1 square.
Step 14. 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: column 4 is down to one square, putting a queen on row 6, column 4; khaki has one square left, so its queen takes row 8, column 5; pale yellow has one square left, so its queen takes row 7, column 9; rose has one square left, so its queen takes row 12, column 7; sea green has one square left, so its queen takes row 10, column 6. 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 6.
The board after step 14 — 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 #120
This is puzzle number 120 in the 12x12 collection, rated easy. 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 #120 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 #120 are: amber (1 square), teal (5 squares), mint (6 squares), rose (6 squares), indigo (7 squares), blue (7 squares), orange (7 squares), sea green (10 squares), slate (11 squares), khaki (12 squares), pale yellow (29 squares), red (43 squares). An even split would hand every color 12 squares, so the amber region is running 11 squares under that average while the red region is the roomiest area on the grid with 43 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Amber is working with 1 square while red has 43 to spare, a gap of 42. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The amber region is the most compact color here, filling 100% of the 1×1 box that encloses it, while red is the most scattered at 39% of its 11×10 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
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 easy board.
Amber: 1 square across rows 2–2, columns 3–3. It never leaves row 2, so its queen is locked to that row.
Teal covers 5 squares, spanning 2 rows and 3 columns (rows 11–12, columns 1–3).
Mint occupies 6 squares within rows 3–4, columns 9–12.
Rose: 6 squares across rows 11–12, columns 7–10.
Indigo covers 7 squares, spanning 2 rows and 4 columns (rows 1–2, columns 9–12).
Blue occupies 7 squares within rows 1–3, columns 6–9.
Orange: 7 squares across rows 9–12, columns 11–12.
Sea green covers 10 squares, spanning 4 rows and 5 columns (rows 9–12, columns 4–8).
Slate occupies 11 squares within rows 1–6, columns 1–2.
Khaki: 12 squares across rows 6–11, columns 3–5.
Pale yellow covers 29 squares, spanning 7 rows and 7 columns (rows 5–11, columns 6–12).
Red occupies 43 squares within rows 1–11, columns 1–10.
Where to start on this board
The most constrained color is where a solve should begin, and on #120 that is amber with 1 square. It reaches from row 2 to row 2 and from column 3 to column 3 — 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 amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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, mint, teal 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 #120
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 4, 5, 7 and 8 are the narrowest, touched by only 3 colors. Columns 1, 2, 4 and 5 are the tightest columns, 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 11 is the crowded extreme at 7 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.
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 #120 is rated easy
The easy label comes out of four measurable things about #120: two of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 42. Boards that score tight on those measures give up their first queen fast.
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.
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 4 on this board.
A non-spoiling distribution check: solved, #120 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 #120?
Puzzle #120 is rated easy. 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 #120 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #120, 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 #120?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.