11x11 Queens Puzzle #199
Difficulty: hard. Place 11 queens on this 11x11 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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #199
What follows is a complete solve of puzzle #199, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 11 queen placements and 7 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 columns.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 5, column 1 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 1, the rest of the slate region and every square adjacent to it — diagonals included.
Step 2. All of the red region's remaining squares (4 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 3. Only row 11, column 10 is still open in teal, and since each colour must take a queen, that settles it. Everything else in row 11, in column 10, in teal and in the ring around that square is now dead.
Step 4. The indigo region is down to one open square, at row 1, column 9. Every colour holds exactly one queen, so that square is forced. Row 1 and column 9 are now spoken for, along with the squares touching that queen.
Step 5. Amber cannot leave row 2 — every one of its open squares (4 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 3 squares in all.
The board after step 5 — 3 of 11 queens placed. Step 6. The pale yellow region has 4 squares left, spread across rows 4, 6, and 7, columns 5 and 6. 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. Blue and mint are now boxed into rows 3 and 4 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 4 squares at once.
Step 8. The red region is down to one open square, at row 6, column 11. Every colour holds exactly one queen, so that square is forced. Row 6 and column 11 are now spoken for, along with the squares touching that queen.
Step 9. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 6 squares in all.
The board after step 9 — 4 of 11 queens placed. Step 10. The khaki region is down to one open square, at row 8, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 7, the remaining khaki squares, and the ring of neighbours around row 8, column 7.
Step 11. Only row 7, column 5 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 5, in pale yellow and in the ring around that square is now dead.
Step 12. 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: 3 squares come off.
Step 13. Mint and sea green are now boxed into columns 6 and 8 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 1 square at once.
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: amber has one square left, so its queen takes row 2, column 4; blue has one square left, so its queen takes row 3, column 2; mint has one square left, so its queen takes row 4, column 8; orange has one square left, so its queen takes row 9, column 3; 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 — 11 of 11 queens placed.
That completes the board: 11 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 11x11 Queens puzzle #199
11x11 puzzle #199 is rated hard. Eleven colored regions cover its 121 squares, and your job is to seat eleven queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Like every board on this site, #199 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 #199 are: slate (1 square), indigo (5 squares), teal (5 squares), red (6 squares), pale yellow (6 squares), amber (9 squares), mint (13 squares), blue (14 squares), sea green (15 squares), khaki (16 squares), orange (31 squares). An even split would hand every color 11 squares, so the slate region is running 10 squares under that average while the orange region is the roomiest area on the grid with 31 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Slate is working with 1 square while orange has 31 to spare, a gap of 30. Attack the cramped end and the roomy regions tend to resolve themselves.
Look at arrangement as well as area. Slate is the densest region on this grid at 100% of a 1×1 frame; mint is the loosest, occupying only 52% of its 5×5 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 hard board.
Slate covers 1 square, spanning 1 row and 1 column (rows 5–5, columns 1–1). It never leaves row 5, so its queen is locked to that row.
Indigo occupies 5 squares within rows 1–3, columns 9–11.
Teal: 5 squares across rows 8–11, columns 10–11.
Red covers 6 squares, spanning 5 rows and 2 columns (rows 2–6, columns 10–11).
Pale yellow occupies 6 squares within rows 4–7, columns 5–6.
Amber: 9 squares across rows 1–2, columns 3–7.
Mint covers 13 squares, spanning 5 rows and 5 columns (rows 1–5, columns 6–10).
Blue occupies 14 squares within rows 1–4, columns 1–5.
Sea green: 15 squares across rows 8–11, columns 5–9.
Khaki covers 16 squares, spanning 6 rows and 5 columns (rows 5–10, columns 7–11).
Orange occupies 31 squares within rows 4–11, columns 1–5.
Where to start on this board
The most constrained color is where a solve should begin, and on #199 that is slate with 1 square. It reaches from row 5 to row 5 and from column 1 to column 1 — 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 slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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. Amber is no more than two rows tall, so its queen is 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 #199
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 7 and 11 are the narrowest, touched by only 3 colors. Column 2 is the tightest column, with 2 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 10 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 eleven queens to seat and eleven regions competing over 121 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 11x11 boards quickly and players who stall halfway.
Resist the plausible-looking queen. On #199 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 #199 is rated hard
The hard label comes out of four measurable things about #199: 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 30. Boards that score tight on those measures give up their first queen fast.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
If #199 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 11x11
At 11x11 you are managing 121 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 column 2 on this board.
As a sanity check rather than a spoiler: the finished solution to #199 puts 4 queens on the outer border and 7 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.
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Questions about this puzzle
How hard is 11x11 Queens puzzle #199?
Puzzle #199 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 11x11 puzzle #199 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #199, has been verified to have exactly one valid arrangement of eleven queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #199?
Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.