11x11 Queens Puzzle #190
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #190
What follows is a complete solve of puzzle #190, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 11 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 confined to one line, region shadow, last square in a row.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Only row 1, column 11 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 11, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The blue region is down to one open square, at row 3, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 10, the remaining blue squares, and the ring of neighbours around row 3, column 10.
Step 3. Amber cannot leave row 2 — every one of its open squares (3 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 5 squares in all.
The board after step 3 — 2 of 11 queens placed. Step 4. All of the mint region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 9 squares come off.
Step 5. Slate is down to 4 candidates in rows 5–7, columns 8 and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
Step 6. All of the sea green region's remaining squares (3 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
The board after step 6 — 2 of 11 queens placed. Step 7. 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: slate has one square left, so its queen takes row 5, column 8; mint has one square left, so its queen takes row 4, column 1; red has one square left, so its queen takes row 6, column 6; amber has one square left, so its queen takes row 2, 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 2, column 2.
Step 8. 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: 2 squares in all.
Step 9. 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: 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 3; row 9 is down to one square, putting a queen on row 9, column 7; teal has one square left, so its queen takes row 11, column 4; sea green has one square left, so its queen takes row 10, column 9. 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 9.
The board after step 9 — 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 #190
Board #190 of the 11x11 bank carries a hard rating. Its 121 squares are shared between eleven colored regions, and the solution places eleven queens: one per row, one per column, one per region, none of them side by side or corner to corner.
As with every puzzle in this collection, #190 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 #190 are: indigo (1 square), mint (4 squares), blue (9 squares), slate (9 squares), pale yellow (10 squares), teal (11 squares), amber (12 squares), khaki (13 squares), orange (15 squares), sea green (17 squares), red (20 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the red region is the roomiest area on the grid with 20 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 1 place to put its queen; red has 20. The spread between them on this board is 19 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×1 frame; blue is the loosest, occupying only 45% of its 5×4 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Below is every color on #190 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Indigo covers 1 square, spanning 1 row and 1 column (rows 1–1, columns 11–11). It never leaves row 1, so its queen is locked to that row.
Mint occupies 4 squares within rows 3–5, columns 1–2.
Blue: 9 squares across rows 1–5, columns 8–11.
Slate covers 9 squares, spanning 6 rows and 2 columns (rows 2–7, columns 8–9).
Pale yellow occupies 10 squares within rows 5–7, columns 1–5.
Teal: 11 squares across rows 10–11, columns 1–8.
Amber covers 12 squares, spanning 3 rows and 6 columns (rows 1–3, columns 1–6).
Khaki occupies 13 squares within rows 7–10, columns 1–7.
Orange: 15 squares across rows 7–10, columns 3–9.
Sea green covers 17 squares, spanning 8 rows and 3 columns (rows 4–11, columns 9–11).
Red occupies 20 squares within rows 1–6, columns 2–8.
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 1 square inside a 1×1 window running from row 1 to row 1 and column 11 to column 11. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
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. Teal 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 #190
A quick way to find the next move is to count how many different colors touch each line. On this board, row 11 is the narrowest, touched by only 2 colors. Column 10 is the tightest column, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 5 sits at the far end with 6 colors crossing it; it will almost certainly be among the last to settle.
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.
The whole middle game reduces to two sweeps. Sweep the eleven colors looking for one with a single square left; sweep the eleven rows and eleven columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 11x11 solve from a stalled one.
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 #190 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 19. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
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 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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #190 the place to look for one is around row 11.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 8 queens in the middle, including 1 in a corner. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #190?
Puzzle #190 is rated hard. Its smallest color region holds 1 square, 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 11x11 puzzle #190 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #190, 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 #190?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.