12x12 Queens Puzzle #100
Difficulty: medium. 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.
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Step-by-step solution for puzzle #100
What follows is a complete solve of puzzle #100, 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 region shadow.
Techniques this board needs: last square in a region, region shadow, region confined to one line.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Only row 12, column 12 is still open in rose, and since each colour must take a queen, that settles it. That clears row 12, column 12, the rest of the rose region and every square adjacent to it — diagonals included.
Step 2. Mint is down to 4 candidates in rows 4 and 5, columns 7–9, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about mint itself.
Step 3. Slate cannot leave row 5 — every one of its open squares (3 open squares) sits there. That row belongs to slate, so every square on it owned by another colour is dead: 9 squares in all.
Step 4. The mint region is down to one open square, at row 4, column 7. Every colour holds exactly one queen, so that square is forced. Row 4 and column 7 are now spoken for, along with the squares touching that queen.
The board after step 4 — 2 of 12 queens placed. Step 5. Only row 6, column 10 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 10, the rest of the red region and every square adjacent to it — diagonals included.
Step 6. The sea green region has 4 squares left, spread across rows 10 and 11, columns 1–3. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 7. Only row 11, column 4 is still open in teal, and since each colour must take a queen, that settles it. Everything else in row 11, in column 4, in teal and in the ring around that square is now dead.
Step 8. The sea green region is down to one open square, at row 10, column 2. Every colour holds exactly one queen, so that square is forced. Row 10 and column 2 are now spoken for, along with the squares touching that queen.
The board after step 8 — 5 of 12 queens placed. Step 9. Only row 5, column 3 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 3, the rest of the slate region and every square adjacent to it — diagonals included.
Step 10. Wherever khaki 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 11. Orange cannot leave row 9 — every one of its open squares (2 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 3 squares in all.
Step 12. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: 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 8; orange has one square left, so its queen takes row 9, column 11; amber has one square left, so its queen takes row 2, column 9; indigo has one square left, so its queen takes row 1, column 6; blue has one square left, so its queen takes row 3, column 1. 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 3, column 1.
The board after step 12 — 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 #100
This is puzzle number 100 in the 12x12 collection, rated medium. 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.
As with every puzzle in this collection, #100 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #100 are: rose (1 square), slate (3 squares), mint (4 squares), teal (4 squares), red (5 squares), sea green (6 squares), amber (14 squares), indigo (20 squares), blue (20 squares), pale yellow (20 squares), khaki (23 squares), orange (24 squares). An even split would hand every color 12 squares, so the rose region is running 11 squares under that average while the orange region is the roomiest area on the grid with 24 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Rose is working with 1 square while orange has 24 to spare, a gap of 23. Attack the cramped end and the roomy regions tend to resolve themselves.
Square count is only half the story — how a color is arranged counts too. Slate is the tidiest shape on #100, packing 100% of its 1×3 bounding box, whereas blue straggles across its 8×5 box at just 50%. 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 #100, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Rose covers 1 square, spanning 1 row and 1 column (rows 12–12, columns 12–12). It never leaves row 12, so its queen is locked to that row.
Slate occupies 3 squares within rows 5–5, columns 2–4. It never leaves row 5, so its queen is locked to that row.
Mint: 4 squares across rows 4–5, columns 7–9.
Teal covers 4 squares, spanning 2 rows and 2 columns (rows 11–12, columns 3–4).
Red occupies 5 squares within rows 4–6, columns 8–10.
Sea green: 6 squares across rows 10–12, columns 1–3.
Amber covers 14 squares, spanning 7 rows and 4 columns (rows 1–7, columns 9–12).
Indigo occupies 20 squares within rows 1–5, columns 4–11.
Blue: 20 squares across rows 1–8, columns 1–5.
Pale yellow covers 20 squares, spanning 4 rows and 8 columns (rows 6–9, columns 5–12).
Khaki occupies 23 squares within rows 6–11, columns 1–6.
Orange: 24 squares across rows 9–12, columns 5–12.
Where to start on this board
The most constrained color is where a solve should begin, and on #100 that is rose with 1 square. It reaches from row 12 to row 12 and from column 12 to column 12 — 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 rose never leaves row 12, its queen must be in that row — and that instantly settles row 12 for everyone else. Sweep along it and X out every square that is not rose. 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. Slate, mint 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 #100
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3, 8, 9 and 10 are the narrowest, touched by only 3 colors. Column 1 is the tightest column, 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 5 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
With twelve queens to seat and twelve regions competing over 144 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 12x12 boards quickly and players who stall halfway.
Resist the plausible-looking queen. On #100 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #100 is rated medium
The rating reflects how much the board concedes up front. Puzzle #100 has three 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 23 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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 1 on this board.
As a sanity check rather than a spoiler: the finished solution to #100 puts 3 queens on the outer border and 9 queens in the interior, 1 of them in an actual 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.
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Questions about this puzzle
How hard is 12x12 Queens puzzle #100?
Puzzle #100 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #100 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #100, 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 #100?
Start with the rose region — the most constrained color on this board, with 1 square spanning rows 12–12 and columns 12–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.