11x11 Queens Puzzle #152

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 15-step reasoning is written out below.

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Step-by-step solution for puzzle #152

What follows is a complete solve of puzzle #152, 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 pairing argument on rows.

Techniques this board needs: last square in a region, region shadow, pairing argument on rows, region confined to one line.

Show the full walkthrough (8 steps) — contains the solution

  1. Step 1. Only row 11, column 6 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 6, the rest of the teal region and every square adjacent to it — diagonals included.

  2. Step 2. The sea green region is down to one open square, at row 10, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 10, the remaining sea green squares, and the ring of neighbours around row 10, column 10.

  3. Step 3. The indigo region has 7 squares left, spread across rows 1–3, columns 3–5. 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.

  4. Step 4. Wherever slate ends up among its 2 squares, the same squares fall within reach of it — 4 squares in total, impossible regardless of how the colour resolves.

    Puzzle #152 after step 4: 2 of 11 queens placed
    The board after step 4 — 2 of 11 queens placed.

  5. Step 5. Indigo, amber, blue, and mint are now boxed into rows 1–4 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 5 squares at once.

  6. Step 6. 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 5; red has one square left, so its queen takes row 6, column 3; indigo has one square left, so its queen takes row 1, column 4; amber has one square left, so its queen takes row 2, column 8. 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 8.

  7. Step 7. All of the mint region's remaining squares (2 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.

  8. Step 8. 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 9; orange has one square left, so its queen takes row 9, column 7; pale yellow has one square left, so its queen takes row 7, column 1; 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 11. 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 4, column 11.

    Puzzle #152 after step 8: 11 of 11 queens placed
    The board after step 8 — 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 #152

This is puzzle number 152 in the 11x11 collection, rated hard. 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 #152 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 #152 are: teal (1 square), sea green (3 squares), slate (5 squares), indigo (7 squares), blue (7 squares), red (9 squares), amber (10 squares), mint (13 squares), khaki (17 squares), pale yellow (20 squares), orange (29 squares). An even split would hand every color 11 squares, so the teal region is running 10 squares under that average while the orange region is the roomiest area on the grid with 29 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 orange has 29 to spare, a gap of 28. Attack the cramped end and the roomy regions tend to resolve themselves.

A region's outline can constrain it more than its size does. Here teal is the most solid, filling 100% of its 1×1 box, and red the most diffuse at 45% of its 5×4 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 #152, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Teal occupies 1 square within rows 11–11, columns 6–6. It never leaves row 11, so its queen is locked to that row.

Sea green: 3 squares across rows 10–11, columns 10–11.

Slate covers 5 squares, spanning 3 rows and 3 columns (rows 4–6, columns 5–7).

Indigo occupies 7 squares within rows 1–3, columns 3–5.

Blue: 7 squares across rows 1–4, columns 1–2.

Red covers 9 squares, spanning 5 rows and 4 columns (rows 2–6, columns 2–5).

Amber occupies 10 squares within rows 1–3, columns 6–11.

Mint: 13 squares across rows 2–5, columns 7–11.

Khaki covers 17 squares, spanning 7 rows and 4 columns (rows 4–10, columns 8–11).

Pale yellow occupies 20 squares within rows 5–10, columns 1–7.

Orange: 29 squares across rows 6–11, columns 1–9.

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 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 #152.

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. Sea green 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 #152

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 7, 8, 9 and 11 are the narrowest, touched by only 3 colors. Column 1 is the tightest column, 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 6, meeting 5 colors, is the opposite case — the busiest line on #152 and the last one you should expect to crack.

Working through the middle game

The middle of #152 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.

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 #152 is rated hard

The rating reflects how much the board concedes up front. Puzzle #152 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 28 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.

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.

Here is a shape check that gives nothing away: when #152 is solved, 4 queens sit on the outer edge of the grid and 7 sit inside it, and no queen lands 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

  1. The board is an N×N grid divided into N colored regions.
  2. Place exactly one queen (♛) in each row, each column, and each colored region.
  3. No two queens may touch each other — not horizontally, vertically, or diagonally.
  4. 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.
  5. 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 #152?

Puzzle #152 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 #152 have only one solution?

Yes. Every puzzle in the 11x11 collection, including #152, 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 #152?

Start with the teal region — the most constrained color on this board, with 1 square spanning rows 11–11 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.