12x12 Queens Puzzle #102
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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #102
What follows is a complete solve of puzzle #102, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 12 queen placements and 8 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: region confined to one line, last square in a region, region shadow, last square in a column.
Show the full walkthrough (16 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 12 squares in all.
Step 2. The amber region is down to one open square, at row 2, column 12. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 12, the remaining amber squares, and the ring of neighbours around row 2, column 12.
Step 3. Rose cannot leave row 12 — every one of its open squares (2 open squares) sits there. That row belongs to rose, so every square on it owned by another colour is dead: 11 squares in all.
Step 4. All of the teal region's remaining squares (4 open squares) lie in row 11. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 5. Only row 10, column 10 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 10, the rest of the sea green region and every square adjacent to it — diagonals included.
The board after step 5 — 2 of 12 queens placed. Step 6. The orange region is down to one open square, at row 9, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 1, the remaining orange squares, and the ring of neighbours around row 9, column 1.
Step 7. Only row 12, column 2 is still open in rose, and since each colour must take a queen, that settles it. Everything else in row 12, in column 2, in rose and in the ring around that square is now dead.
Step 8. Blue is down to 4 candidates in rows 3 and 4, columns 7–9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 9. The mint region has 6 squares left, spread across rows 3–5, columns 3–5. 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 red 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: 2 squares come off.
Step 11. Only row 8, column 9 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 9, in khaki and in the ring around that square is now dead.
The board after step 11 — 5 of 12 queens placed. Step 12. 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. Row 1 and column 8 are now spoken for, along with the squares touching that queen.
Step 13. Only row 3, column 7 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 7, the rest of the blue region and every square adjacent to it — diagonals included.
Step 14. Mint is down to 3 candidates in rows 4 and 5, columns 3 and 5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 15. The pale yellow region has 4 squares left, spread across rows 5–7, columns 3 and 4. 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 16. 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 7, column 4; column 3 is down to one square, putting a queen on row 4, column 3; red has one square left, so its queen takes row 6, column 11; slate has one square left, so its queen takes row 5, column 6; teal has one square left, so its queen takes row 11, 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 11, column 5.
The board after step 16 — 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 #102
Board #102 of the 12x12 bank carries a easy rating. Its 144 squares are shared between twelve colored regions, and the solution places twelve queens: one per row, one per column, one per region, none of them side by side or corner to corner.
Like every board on this site, #102 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 #102 are: indigo (2 squares), rose (2 squares), amber (3 squares), red (9 squares), orange (9 squares), sea green (10 squares), teal (10 squares), khaki (12 squares), blue (17 squares), mint (20 squares), slate (23 squares), pale yellow (27 squares). An even split would hand every color 12 squares, so the indigo region is running 10 squares under that average while the pale yellow region is the roomiest area on the grid with 27 squares.
Every color takes one queen and one only, whatever its size — which is why the 25 square difference between indigo and pale yellow 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 1×2 frame; blue is the loosest, occupying only 53% of its 4×8 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 easy board.
Indigo: 2 squares across rows 1–1, columns 8–9. It never leaves row 1, so its queen is locked to that row.
Rose covers 2 squares, spanning 1 row and 2 columns (rows 12–12, columns 1–2). It never leaves row 12, so its queen is locked to that row.
Amber occupies 3 squares within rows 1–2, columns 11–12.
Red: 9 squares across rows 4–7, columns 10–12.
Orange covers 9 squares, spanning 3 rows and 4 columns (rows 9–11, columns 1–4).
Sea green occupies 10 squares within rows 10–12, columns 9–12.
Teal: 10 squares across rows 11–12, columns 3–8.
Khaki covers 12 squares, spanning 3 rows and 5 columns (rows 8–10, columns 8–12).
Blue occupies 17 squares within rows 1–4, columns 5–12.
Mint: 20 squares across rows 1–5, columns 1–5.
Slate covers 23 squares, spanning 5 rows and 8 columns (rows 3–7, columns 4–11).
Pale yellow occupies 27 squares within rows 5–10, columns 1–8.
Where to start on this board
Indigo is the natural opening on #102: it is the smallest region on the grid at 2 squares, boxed into rows 1–1 and columns 8–9. Since one of those squares must hold a queen, that block of 1 row and 2 columns is the most contested part of the board.
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, amber and teal 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 #102
A quick way to find the next move is to count how many different colors touch each line. On this board, row 8 is the narrowest, touched by only 2 colors. Columns 1, 2, 3, 6 and 7 are the tightest columns, with 4 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 11 rows. Row 10, meeting 4 colors, is the opposite case — the busiest line on #102 and the last one you should expect to crack.
Working through the middle game
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
Keep alternating between two views of the board. In the region view you ask which of the twelve colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 12x12 board unwinds.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #102 is rated easy
The easy label comes out of four measurable things about #102: two of its regions are locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 2 colors, and its largest and smallest regions differ by 25. Boards that score tight on those measures give up their first queen fast.
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.
If #102 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.
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 #102 is row 8.
Here is a shape check that gives nothing away: when #102 is solved, 4 queens sit on the outer edge of the grid and 8 sit inside it, and no queen lands 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 #102?
Puzzle #102 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #102 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #102, 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 #102?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–1 and columns 8–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.