12x12 Queens Puzzle #101
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.
Previous puzzle · All 12x12 puzzles · Next puzzle
Step-by-step solution for puzzle #101
What follows is a complete solve of puzzle #101, 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 region shadow.
Techniques this board needs: last square in a region, region confined to one line, region shadow, last square in a row.
Show the full walkthrough (19 steps) — contains the solution
Step 1. Only row 6, column 5 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 5, the rest of the red 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: 9 squares come off.
Step 3. Orange cannot leave column 6 — 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: 8 squares in all.
Step 4. Wherever sea green ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Only row 11, column 1 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 1, the rest of the teal region and every square adjacent to it — diagonals included.
The board after step 5 — 2 of 12 queens placed. Step 6. The amber region has 3 squares left, spread across rows 2 and 3, 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 7. Sea green cannot leave column 3 — every one of its open squares (2 open squares) sits there. That column belongs to sea green, so every square in it owned by another colour is dead: 6 squares in all.
Step 8. All of the amber region's remaining squares (2 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
Step 9. 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: 6 squares in all.
Step 10. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: sea green has one square left, so its queen takes row 10, column 3; orange has one square left, so its queen takes row 9, column 6; khaki has one square left, so its queen takes row 8, column 4; rose has one square left, so its queen takes row 12, column 7. 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 7.
The board after step 10 — 6 of 12 queens placed. Step 11. All of the slate region's remaining squares (2 open squares) lie in column 12. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
Step 12. 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: 1 square in all.
Step 13. The blue region is down to one open square, at row 3, column 11. Every colour holds exactly one queen, so that square is forced. Row 3 and column 11 are now spoken for, along with the squares touching that queen.
Step 14. Only row 1, column 10 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 10, the rest of the indigo region and every square adjacent to it — diagonals included.
The board after step 14 — 8 of 12 queens placed. Step 15. The amber region is down to one open square, at row 2, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 2, the remaining amber squares, and the ring of neighbours around row 2, column 2.
Step 16. Wherever mint 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 17. Row 4 has a single open square left, at column 8 in the mint region. Every row needs a queen, so this one is forced. Cross out the whole of row 4 and column 8, the remaining mint squares, and the ring of neighbours around row 4, column 8.
Step 18. Only row 7, column 9 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 9, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 19. The slate region is down to one open square, at row 5, column 12. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 12, the remaining slate squares, and the ring of neighbours around row 5, column 12.
The board after step 19 — 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 #101
Puzzle #101 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, #101 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 #101 are: red (1 square), orange (2 squares), teal (2 squares), indigo (3 squares), blue (6 squares), sea green (6 squares), amber (10 squares), rose (11 squares), slate (15 squares), pale yellow (26 squares), mint (30 squares), khaki (32 squares). An even split would hand every color 12 squares, so the red region is running 11 squares under that average while the khaki region is the roomiest area on the grid with 32 squares.
Every color takes one queen and one only, whatever its size — which is why the 31 square difference between red 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.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #101, packing 100% of its 1×3 bounding box, whereas slate straggles across its 8×5 box at just 38%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Here is the full footprint of every color on puzzle #101, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Red occupies 1 square within rows 6–6, columns 5–5. It never leaves row 6, so its queen is locked to that row.
Orange: 2 squares across rows 9–10, columns 6–6. It sits wholly inside column 6, so its queen must be in that column.
Teal covers 2 squares, spanning 1 row and 2 columns (rows 11–11, columns 1–2). It never leaves row 11, so its queen is locked to that row.
Indigo occupies 3 squares within rows 1–1, columns 10–12. It never leaves row 1, so its queen is locked to that row.
Blue: 6 squares across rows 2–4, columns 10–12.
Sea green covers 6 squares, spanning 3 rows and 3 columns (rows 10–12, columns 1–3).
Amber occupies 10 squares within rows 1–4, columns 1–4.
Rose: 11 squares across rows 10–12, columns 4–9.
Slate covers 15 squares, spanning 8 rows and 5 columns (rows 5–12, columns 8–12).
Pale yellow occupies 26 squares within rows 3–10, columns 8–11.
Mint: 30 squares across rows 1–7, columns 3–9.
Khaki covers 32 squares, spanning 7 rows and 7 columns (rows 4–10, columns 1–7).
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 5 and 5. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #101.
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, teal and orange 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 #101
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 8 and 12 are the narrowest, touched by only 3 colors. Columns 7 and 12 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 10 is the crowded extreme at 6 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.
The whole middle game reduces to two sweeps. Sweep the twelve colors looking for one with a single square left; sweep the twelve rows and twelve columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 12x12 solve from a stalled one.
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 #101 is rated easy
The rating reflects how much the board concedes up front. Puzzle #101 has five regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 31 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
If #101 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 #101 is row 1.
A non-spoiling distribution check: solved, #101 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 12x12 Queens puzzle #101?
Puzzle #101 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 #101 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #101, 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 #101?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.