11x11 Queens Puzzle #213

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 18-step reasoning is written out below.

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Step-by-step solution for puzzle #213

What follows is a complete solve of puzzle #213, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 11 queen placements and 7 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, region confined to one line, pairing argument on rows, pairing argument on columns, last square in a row.

Show the full walkthrough (11 steps) — contains the solution

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

  2. Step 2. The mint region is down to one open square, at row 4, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 11, the remaining mint squares, and the ring of neighbours around row 4, column 11.

  3. Step 3. The red region has 2 squares left, spread across rows 5 and 6, columns 9 and 10. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.

  4. Step 4. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 10 squares come off.

    Puzzle #213 after step 4: 2 of 11 queens placed
    The board after step 4 — 2 of 11 queens placed.

  5. Step 5. Sea green is down to 3 candidates in rows 10 and 11, columns 2 and 3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about sea green itself.

  6. Step 6. Here is the pairing argument. The amber, blue, and slate regions have no open squares outside rows 2, 3, and 5 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 8 squares come off in one stroke.

  7. Step 7. Only row 6, column 10 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 10, in red and in the ring around that square is now dead.

    Puzzle #213 after step 7: 3 of 11 queens placed
    The board after step 7 — 3 of 11 queens placed.

  8. Step 8. All of the khaki region's remaining squares (4 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.

  9. Step 9. Orange cannot leave row 9 — every one of its open squares (4 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 4 squares in all.

  10. Step 10. Here is the pairing argument. The pale yellow and sea green regions have no open squares outside columns 2 and 3 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 7 squares come off in one stroke.

  11. Step 11. 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: amber has one square left, so its queen takes row 2, column 4; orange has one square left, so its queen takes row 9, column 5; row 5 is down to one square, putting a queen on row 5, column 8; blue has one square left, so its queen takes row 3, column 9; khaki has one square left, so its queen takes row 8, column 7; teal has one square left, so its queen takes row 11, column 6; sea green has one square left, so its queen takes row 10, column 2; pale yellow has one square left, so its queen takes row 7, column 3. 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 3.

    Puzzle #213 after step 11: 11 of 11 queens placed
    The board after step 11 — 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 #213

Puzzle #213 is one of the medium-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 #213, 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 #213 are: indigo (1 square), mint (1 square), pale yellow (4 squares), sea green (6 squares), slate (8 squares), orange (9 squares), red (11 squares), blue (14 squares), teal (20 squares), amber (21 squares), khaki (26 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 26 squares.

Every color takes one queen and one only, whatever its size — which is why the 25 square difference between indigo and khaki 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.

Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #213, packing 100% of its 1×1 bounding box, whereas red straggles across its 8×3 box at just 46%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a medium board.

Indigo: 1 square across rows 1–1, columns 1–1. It never leaves row 1, so its queen is locked to that row.

Mint covers 1 square, spanning 1 row and 1 column (rows 4–4, columns 11–11). It never leaves row 4, so its queen is locked to that row.

Pale yellow occupies 4 squares within rows 7–8, columns 1–3.

Sea green: 6 squares across rows 9–11, columns 1–3.

Slate covers 8 squares, spanning 4 rows and 3 columns (rows 2–5, columns 6–8).

Orange occupies 9 squares within rows 7–10, columns 2–5.

Red: 11 squares across rows 4–11, columns 9–11.

Blue covers 14 squares, spanning 4 rows and 5 columns (rows 1–4, columns 7–11).

Teal occupies 20 squares within rows 8–11, columns 4–10.

Amber: 21 squares across rows 1–6, columns 1–6.

Khaki covers 26 squares, spanning 7 rows and 7 columns (rows 2–8, columns 4–10).

Where to start on this board

Indigo is the natural opening on #213: it is the smallest region on the grid at 1 square, boxed into rows 1–1 and columns 1–1. 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 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. Mint and pale yellow 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 #213

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 11 are the narrowest, touched by only 3 colors. Column 11 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 4, meeting 6 colors, is the opposite case — the busiest line on #213 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 #213 is rated medium

The medium label comes out of four measurable things about #213: four of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 25. Boards that score tight on those measures give up their first queen fast.

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 #213 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 #213 is row 1.

Here is a shape check that gives nothing away: when #213 is solved, 3 queens sit on the outer edge of the grid and 8 sit inside it, with 1 queen 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 #213?

Puzzle #213 is rated medium. 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 #213 have only one solution?

Yes. Every puzzle in the 11x11 collection, including #213, 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 #213?

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