11x11 Queens Puzzle #198
Difficulty: easy. 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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #198
What follows is a complete solve of puzzle #198, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 11 queen placements and 6 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, last square in a column.
Show the full walkthrough (12 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 teal region is down to one open square, at row 11, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 1, the remaining teal squares, and the ring of neighbours around row 11, column 1.
Step 3. Only row 9, column 2 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 2, in orange and in the ring around that square is now dead.
Step 4. Wherever blue ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
The board after step 4 — 3 of 11 queens placed. Step 5. Pale yellow is down to 4 candidates in rows 7 and 8, columns 4–6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 6. All of the khaki region's remaining squares (2 open squares) lie in column 10. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
Step 7. Blue cannot leave row 3 — every one of its open squares (2 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 8 squares in all.
Step 8. All of the amber region's remaining squares (2 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
The board after step 8 — 3 of 11 queens placed. Step 9. Only row 4, column 7 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 7, the rest of the mint region and every square adjacent to it — diagonals included.
Step 10. The blue region is down to one open square, at row 3, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 9, the remaining blue squares, and the ring of neighbours around row 3, column 9.
Step 11. Sea green cannot leave row 10 — every one of its open squares (3 open squares) sits there. That row belongs to sea green, so every square on it owned by another colour is dead: 2 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 10; pale yellow has one square left, so its queen takes row 7, column 6; column 8 is down to one square, putting a queen on row 6, column 8; slate has one square left, so its queen takes row 5, column 3; amber has one square left, so its queen takes row 2, column 4; sea green has one square left, so its queen takes row 10, 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 10, column 5.
The board after step 12 — 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 #198
Board #198 of the 11x11 bank carries a easy 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, #198 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 #198 are: indigo (1 square), teal (1 square), orange (6 squares), pale yellow (7 squares), mint (10 squares), khaki (10 squares), blue (12 squares), sea green (13 squares), amber (14 squares), slate (16 squares), red (31 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 31 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So indigo, with 1 square, is under far more pressure than red with 31. A 30-square gap like this one rewards players who start where the choices are fewest.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and pale yellow the most diffuse at 47% of its 3×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Here is the full footprint of every color on puzzle #198, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo: 1 square across rows 1–1, columns 11–11. It never leaves row 1, so its queen is locked to that row.
Teal covers 1 square, spanning 1 row and 1 column (rows 11–11, columns 1–1). It never leaves row 11, so its queen is locked to that row.
Orange occupies 6 squares within rows 8–11, columns 1–2.
Pale yellow: 7 squares across rows 7–9, columns 2–6.
Mint covers 10 squares, spanning 4 rows and 5 columns (rows 1–4, columns 5–9).
Khaki occupies 10 squares within rows 6–11, columns 10–11.
Blue: 12 squares across rows 1–5, columns 8–11.
Sea green covers 13 squares, spanning 3 rows and 5 columns (rows 9–11, columns 3–7).
Amber occupies 14 squares within rows 1–3, columns 1–5.
Slate: 16 squares across rows 4–7, columns 1–5.
Red covers 31 squares, spanning 9 rows and 7 columns (rows 3–11, columns 4–10).
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 #198
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 5 and 6 are the narrowest, touched by only 3 colors. Columns 7, 8, 9, 10 and 11 are the tightest columns, with 3 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 11, meeting 5 colors, is the opposite case — the busiest line on #198 and the last one you should expect to crack.
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.
Two checks, run alternately, will carry you through the 121 squares of this grid. First: has any of the eleven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 11x11 boards almost always run one of those checks and forget the other.
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 #198 is rated easy
The rating reflects how much the board concedes up front. Puzzle #198 has four 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 30 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.
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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #198, start hunting for it near row 2.
Here is a shape check that gives nothing away: when #198 is solved, 2 queens sit on the outer edge of the grid and 9 sit inside it, with 2 queens 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 11x11 Queens puzzle #198?
Puzzle #198 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #198 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #198, 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 #198?
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.