11x11 Queens Puzzle #48
Difficulty: medium. 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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #48
What follows is a complete solve of puzzle #48, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 11 queen placements and 8 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 shadow, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (12 steps) — contains the solution
Step 1. 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.
Step 2. Amber is down to 3 candidates in rows 1 and 2, columns 10 and 11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The slate region has 4 squares left, spread across rows 3–5, columns 3 and 4. 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 4. Wherever orange ends up among its 5 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 — 1 of 11 queens placed. Step 5. Sea green is down to 4 candidates in rows 8–10, columns 8 and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about sea green itself.
Step 6. Here is the pairing argument. The indigo and amber regions have no open squares outside rows 1 and 2 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 9 squares come off in one stroke.
Step 7. Khaki, orange, and sea green are now boxed into rows 8–10 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 12 squares at once.
Step 8. Here is the pairing argument. The slate, red, and khaki regions have no open squares outside columns 2–4 — 3 colours confined to 3 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 5 squares come off in one stroke.
The board after step 8 — 1 of 11 queens placed. Step 9. Only row 1, column 5 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 5, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 10. The amber region is down to one open square, at row 2, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 11, the remaining amber squares, and the ring of neighbours around row 2, column 11.
Step 11. Blue is down to 3 candidates in rows 3 and 4, columns 7 and 8, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 12. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: mint has one square left, so its queen takes row 4, column 6; blue has one square left, so its queen takes row 3, column 8; slate has one square left, so its queen takes row 5, column 4; sea green has one square left, so its queen takes row 10, column 9; orange has one square left, so its queen takes row 9, column 7; khaki has one square left, so its queen takes row 8, column 3; red has one square left, so its queen takes row 6, column 2; pale yellow has one square left, so its queen takes row 7, column 10. 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 7, column 10.
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 #48
This is puzzle number 48 in the 11x11 collection, rated medium. The grid holds 121 squares split between eleven colored regions, and a finished board carries eleven queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
Puzzle #48 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #48 are: teal (1 square), amber (3 squares), slate (4 squares), orange (7 squares), sea green (9 squares), indigo (10 squares), khaki (10 squares), mint (13 squares), blue (14 squares), red (19 squares), pale yellow (31 squares). An even split would hand every color 11 squares, so the teal region is running 10 squares under that average while the pale yellow 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. Teal is working with 1 square while pale yellow has 31 to spare, a gap of 30. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The teal region is the most compact color here, filling 100% of the 1×1 box that encloses it, while sea green is the most scattered at 45% of its 4×5 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
Region by region
Here is the full footprint of every color on puzzle #48, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Teal: 1 square across rows 11–11, columns 1–1. It never leaves row 11, so its queen is locked to that row.
Amber covers 3 squares, spanning 2 rows and 2 columns (rows 1–2, columns 10–11).
Slate occupies 4 squares within rows 3–5, columns 3–4.
Orange: 7 squares across rows 9–11, columns 5–7.
Sea green covers 9 squares, spanning 4 rows and 5 columns (rows 8–11, columns 7–11).
Indigo occupies 10 squares within rows 1–3, columns 1–5.
Khaki: 10 squares across rows 8–11, columns 2–4.
Mint covers 13 squares, spanning 8 rows and 3 columns (rows 2–9, columns 4–6).
Blue occupies 14 squares within rows 1–4, columns 6–11.
Red: 19 squares across rows 3–10, columns 1–4.
Pale yellow covers 31 squares, spanning 8 rows and 6 columns (rows 3–10, columns 6–11).
Where to start on this board
Open on the tightest color. Here that is teal, confined to 1 square between rows 11 and 11 and columns 1 and 1. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #48.
Because teal never leaves row 11, its queen must be in that row — and that instantly settles row 11 for everyone else. Sweep along it and X out every square that is not teal. 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 #48
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 6 and 7 are the narrowest, touched by only 3 colors. Columns 1, 2, 5, 8 and 9 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 10 rows. Row 9 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.
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 #48 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 #48 is rated medium
The rating reflects how much the board concedes up front. Puzzle #48 has two 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.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a medium board from the rest.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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 row 1 on this board.
A non-spoiling distribution check: solved, #48 carries 3 queens on the perimeter against 8 queens inside, 1 of them cornered. 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.
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Questions about this puzzle
How hard is 11x11 Queens puzzle #48?
Puzzle #48 is rated medium. 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 #48 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #48, 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 #48?
Start with the teal region — the most constrained color on this board, with 1 square spanning rows 11–11 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.