11x11 Queens Puzzle #145

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 #145

What follows is a complete solve of puzzle #145, 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 confined to one line, region shadow.

Show the full walkthrough (6 steps) — contains the solution

  1. Step 1. Only row 2, column 11 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 11, the rest of the amber region and every square adjacent to it — diagonals included.

  2. Step 2. All of the indigo region's remaining squares (4 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.

  3. Step 3. 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: 7 squares in all.

    Puzzle #145 after step 3: 1 of 11 queens placed
    The board after step 3 — 1 of 11 queens placed.

  4. Step 4. Wherever mint ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.

  5. Step 5. Slate is down to 3 candidates in rows 4–6, columns 5 and 6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about slate itself.

  6. Step 6. From here the board cascades. Keep alternating the region sweep and the line sweep and 10 queens fall out in order without any new idea being needed: pale yellow has one square left, so its queen takes row 7, column 5; slate has one square left, so its queen takes row 5, column 6; mint has one square left, so its queen takes row 4, column 8; teal has one square left, so its queen takes row 11, column 7; indigo has one square left, so its queen takes row 1, column 9; sea green has one square left, so its queen takes row 10, column 4; blue has one square left, so its queen takes row 3, column 1; 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; orange has one square left, so its queen takes row 9, 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 9, column 10.

    Puzzle #145 after step 6: 11 of 11 queens placed
    The board after step 6 — 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 #145

Puzzle #145 is one of the hard-rated boards in the 11x11 set. Eleven colors divide its 121 squares, and you win by placing eleven queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.

There is exactly one way to finish #145, 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 #145 are: amber (1 square), pale yellow (3 squares), sea green (4 squares), indigo (9 squares), blue (9 squares), teal (9 squares), slate (10 squares), mint (13 squares), khaki (16 squares), red (17 squares), orange (30 squares). An even split would hand every color 11 squares, so the amber region is running 10 squares under that average while the orange region is the roomiest area on the grid with 30 squares.

Every color takes one queen and one only, whatever its size — which is why the 29 square difference between amber and orange 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.

Shape matters as much as size. The amber region is the most compact color here, filling 100% of the 1×1 box that encloses it, while mint is the most scattered at 43% of its 6×5 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

The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.

Amber covers 1 square, spanning 1 row and 1 column (rows 2–2, columns 11–11). It never leaves row 2, so its queen is locked to that row.

Pale yellow occupies 3 squares within rows 5–7, columns 5–5. It sits wholly inside column 5, so its queen must be in that column.

Sea green: 4 squares across rows 10–11, columns 3–5.

Indigo covers 9 squares, spanning 2 rows and 6 columns (rows 1–2, columns 6–11).

Blue occupies 9 squares within rows 1–3, columns 1–4.

Teal: 9 squares across rows 6–11, columns 5–7.

Slate covers 10 squares, spanning 6 rows and 3 columns (rows 1–6, columns 4–6).

Mint occupies 13 squares within rows 2–7, columns 7–11.

Khaki: 16 squares across rows 5–11, columns 1–5.

Red covers 17 squares, spanning 7 rows and 4 columns (rows 3–9, columns 1–4).

Orange occupies 30 squares within rows 4–11, columns 7–11.

Where to start on this board

Amber is the natural opening on #145: it is the smallest region on the grid at 1 square, boxed into rows 2–2 and columns 11–11. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.

Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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 sea green 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 #145

A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 3 colors. Columns 1, 2, 6, 8, 9 and 10 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 6, meeting 7 colors, is the opposite case — the busiest line on #145 and the last one you should expect to crack.

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.

The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.

Why puzzle #145 is rated hard

Ratings track how generous the opening is. On #145 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 29-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.

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 hard board from the rest.

Stuck on #145 despite the hard 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 #145 is row 1.

Here is a shape check that gives nothing away: when #145 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 #145?

Puzzle #145 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.

Does 11x11 puzzle #145 have only one solution?

Yes. Every puzzle in the 11x11 collection, including #145, 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 #145?

Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.