11x11 Queens Puzzle #148
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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #148
What follows is a complete solve of puzzle #148, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 11 queen placements and 4 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 (7 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: orange has one square left, so its queen takes row 9, column 6; khaki has one square left, so its queen takes row 8, column 9; indigo has one square left, so its queen takes row 1, column 8; sea green has one square left, so its queen takes row 10, 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 10, column 1.
Step 2. Blue is down to 3 candidates in rows 2 and 3, columns 2 and 3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 3. All of the red region's remaining squares (2 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
Step 4. Only row 3, column 3 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 3, in blue and in the ring around that square is now dead.
The board after step 4 — 5 of 11 queens placed. Step 5. Amber is down to 2 candidates in rows 2 and 5, columns 4 and 5, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 6. Teal cannot leave row 11 — every one of its open squares (3 open squares) sits there. That row belongs to teal, so every square on it owned by another colour is dead: 2 squares in all.
Step 7. 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: pale yellow has one square left, so its queen takes row 7, column 4; amber has one square left, so its queen takes row 2, column 5; mint has one square left, so its queen takes row 4, column 11; red has one square left, so its queen takes row 6, column 2; slate has one square left, so its queen takes row 5, column 7; teal has one square left, so its queen takes row 11, 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 11, column 10.
The board after step 7 — 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 #148
This is puzzle number 148 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.
There is exactly one way to finish #148, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these eleven regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #148 are: orange (1 square), khaki (2 squares), indigo (3 squares), sea green (4 squares), mint (7 squares), blue (8 squares), red (9 squares), amber (13 squares), teal (14 squares), pale yellow (21 squares), slate (39 squares). An even split would hand every color 11 squares, so the orange region is running 10 squares under that average while the slate region is the roomiest area on the grid with 39 squares.
Every color takes one queen and one only, whatever its size — which is why the 38 square difference between orange and slate is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
A region's outline can constrain it more than its size does. Here khaki is the most solid, filling 100% of its 2×1 box, and slate the most diffuse at 49% of its 10×8 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #148 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.
Orange covers 1 square, spanning 1 row and 1 column (rows 9–9, columns 6–6). It never leaves row 9, so its queen is locked to that row.
Khaki occupies 2 squares within rows 8–9, columns 9–9. It sits wholly inside column 9, so its queen must be in that column.
Indigo: 3 squares across rows 1–2, columns 8–9.
Sea green covers 4 squares, spanning 3 rows and 2 columns (rows 8–10, columns 1–2).
Mint occupies 7 squares within rows 1–4, columns 10–11.
Blue: 8 squares across rows 1–3, columns 1–3.
Red covers 9 squares, spanning 5 rows and 3 columns (rows 4–8, columns 1–3).
Amber occupies 13 squares within rows 1–5, columns 3–6.
Teal: 14 squares across rows 8–11, columns 6–11.
Pale yellow covers 21 squares, spanning 7 rows and 6 columns (rows 5–11, columns 1–6).
Slate occupies 39 squares within rows 1–10, columns 4–11.
Where to start on this board
Open on the tightest color. Here that is orange, confined to 1 square between rows 9 and 9 and columns 6 and 6. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #148.
Because orange never leaves row 9, its queen must be in that row — and that instantly settles row 9 for everyone else. Sweep along it and X out every square that is not orange. 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. Indigo and khaki 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 #148
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 7 is the tightest column, with 2 colors.
A line with few colors is a line close to resolving. Where only 2 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
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
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.
Resist the plausible-looking queen. On #148 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 #148 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 38. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
Stuck on #148 despite the medium rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #148 is row 11.
A non-spoiling distribution check: solved, #148 carries 4 queens on the perimeter against 7 queens inside, with the corners empty. 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 #148?
Puzzle #148 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #148 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #148, 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 #148?
Start with the orange region — the most constrained color on this board, with 1 square spanning rows 9–9 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.