11x11 Queens Puzzle #23

Difficulty: easy. 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 13-step reasoning is written out below.

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Step-by-step solution for puzzle #23

What follows is a complete solve of puzzle #23, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 11 queen placements and 2 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 confined to one line.

Techniques this board needs: last square in a region, region confined to one line.

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

  1. Step 1. Only row 3, column 3 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 3, the rest of the blue region and every square adjacent to it — diagonals included.

  2. Step 2. The orange region is down to one open square, at row 9, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 9, the remaining orange squares, and the ring of neighbours around row 9, column 9.

  3. Step 3. Pale yellow cannot leave column 11 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 8 squares in all.

  4. Step 4. The indigo region is down to one open square, at row 1, column 10. Every colour holds exactly one queen, so that square is forced. Row 1 and column 10 are now spoken for, along with the squares touching that queen.

    Puzzle #23 after step 4: 3 of 11 queens placed
    The board after step 4 — 3 of 11 queens placed.

  5. Step 5. Only row 11, column 8 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 8, the rest of the teal region and every square adjacent to it — diagonals included.

  6. Step 6. The mint region is down to one open square, at row 4, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 7, the remaining mint squares, and the ring of neighbours around row 4, column 7.

  7. Step 7. Amber cannot leave column 1 — every one of its open squares (3 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 3 squares in all.

  8. Step 8. 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: sea green has one square left, so its queen takes row 10, column 2; khaki has one square left, so its queen takes row 8, column 5; red has one square left, so its queen takes row 6, column 6; slate has one square left, so its queen takes row 5, column 4; amber has one square left, so its queen takes row 2, column 1; pale yellow has one square left, so its queen takes row 7, 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 7, column 11.

    Puzzle #23 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 #23

11x11 puzzle #23 is rated easy. Eleven colored regions cover its 121 squares, and your job is to seat eleven queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.

Like every board on this site, #23 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.

How the colors divide this board

From smallest to largest, the regions on puzzle #23 are: blue (1 square), orange (1 square), pale yellow (2 squares), indigo (8 squares), mint (8 squares), sea green (8 squares), teal (9 squares), khaki (10 squares), amber (11 squares), slate (25 squares), red (38 squares). An even split would hand every color 11 squares, so the blue region is running 10 squares under that average while the red region is the roomiest area on the grid with 38 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Blue has only 1 place to put its queen; red has 38. The spread between them on this board is 37 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

Look at arrangement as well as area. Blue is the densest region on this grid at 100% of a 1×1 frame; red is the loosest, occupying only 49% of its 7×11 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

Region by region

Here is the full footprint of every color on puzzle #23, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Blue occupies 1 square within rows 3–3, columns 3–3. It never leaves row 3, so its queen is locked to that row.

Orange: 1 square across rows 9–9, columns 9–9. It never leaves row 9, so its queen is locked to that row.

Pale yellow covers 2 squares, spanning 2 rows and 1 column (rows 7–8, columns 11–11). It sits wholly inside column 11, so its queen must be in that column.

Indigo occupies 8 squares within rows 1–4, columns 9–11.

Mint: 8 squares across rows 1–4, columns 7–10.

Sea green covers 8 squares, spanning 2 rows and 5 columns (rows 10–11, columns 1–5).

Teal occupies 9 squares within rows 9–11, columns 8–11.

Khaki: 10 squares across rows 8–11, columns 5–7.

Amber covers 11 squares, spanning 6 rows and 3 columns (rows 1–6, columns 1–3).

Slate occupies 25 squares within rows 1–6, columns 2–7.

Red: 38 squares across rows 4–10, columns 1–11.

Where to start on this board

The most constrained color is where a solve should begin, and on #23 that is blue with 1 square. It reaches from row 3 to row 3 and from column 3 to column 3 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.

Because blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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. Orange, pale yellow 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 #23

A quick way to find the next move is to count how many different colors touch each line. On this board, row 7 is the narrowest, touched by only 2 colors. Columns 1, 4, 6 and 8 are the tightest columns, with 3 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 4 is the crowded extreme at 5 colors — worth revisiting later, not now.

Working through the middle game

The middle of #23 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.

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.

Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.

Why puzzle #23 is rated easy

The rating reflects how much the board concedes up front. Puzzle #23 has five regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 37 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.

If #23 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.

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.

One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #23 the place to look for one is around row 7.

A non-spoiling distribution check: solved, #23 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

  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 #23?

Puzzle #23 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.

Does 11x11 puzzle #23 have only one solution?

Yes. Every puzzle in the 11x11 collection, including #23, 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 #23?

Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.