11x11 Queens Puzzle #124
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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #124
What follows is a complete solve of puzzle #124, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 11 queen placements and 9 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 proof by contradiction.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows, proof by contradiction, last square in a row, line confined to one region, last square in a column.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 9, column 1 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 1, the rest of the orange region and every square adjacent to it — diagonals included.
Step 2. The teal region is down to one open square, at row 11, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 11, the remaining teal squares, and the ring of neighbours around row 11, column 11.
Step 3. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 7 squares in all.
Step 4. The mint region is down to one open square, at row 4, column 10. Every colour holds exactly one queen, so that square is forced. Row 4 and column 10 are now spoken for, along with the squares touching that queen.
Step 5. Blue cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 5 squares in all.
The board after step 5 — 3 of 11 queens placed. Step 6. The slate region has 3 squares left, spread across rows 2, 3, and 5, columns 4 and 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.
Step 7. Amber, blue, and slate are now boxed into rows 2, 3, and 5 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 9 squares at once.
Step 8. Now a short proof by contradiction. Suppose the amber queen went to row 3, column 5. Follow the forced moves that would create and the blue region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 9. Amber cannot leave column 6 — 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: 4 squares in all.
The board after step 9 — 3 of 11 queens placed. Step 10. Now a short proof by contradiction. Suppose the amber queen went to row 5, column 6. Follow the forced moves that would create and column 8 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 11. Look along row 5: one square survives, row 5, column 4, which belongs to slate. A row cannot be left empty, so the queen goes there. That clears row 5, column 4, the rest of the slate region and every square adjacent to it — diagonals included.
Step 12. Every open square left in row 6 (3 open squares) belongs to the red region. Since that row must contain a queen, red is the colour that supplies it — so red squares anywhere else on the board are out, 3 squares in all.
Step 13. Test row 6, column 8 for red: place a queen there, run the forced consequences through, and column 7 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 14. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: column 8 is down to one square, putting a queen on row 10, column 8; pale yellow has one square left, so its queen takes row 7, column 9; red has one square left, so its queen takes row 6, column 7; khaki has one square left, so its queen takes row 8, column 5; indigo has one square left, so its queen takes row 1, column 3; blue has one square left, so its queen takes row 3, column 2; amber has one square left, so its queen takes row 2, column 6. 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 6.
The board after step 14 — 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 #124
This is puzzle number 124 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.
As with every puzzle in this collection, #124 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #124 are: orange (1 square), teal (1 square), indigo (3 squares), blue (7 squares), amber (9 squares), mint (9 squares), slate (15 squares), sea green (15 squares), pale yellow (16 squares), red (21 squares), khaki (24 squares). An even split would hand every color 11 squares, so the orange region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 24 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Orange is working with 1 square while khaki has 24 to spare, a gap of 23. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×3 box that encloses it, while slate is the most scattered at 43% of its 7×5 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
Below is every color on #124 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 1–1). It never leaves row 9, so its queen is locked to that row.
Teal occupies 1 square within rows 11–11, columns 11–11. It never leaves row 11, so its queen is locked to that row.
Indigo: 3 squares across rows 1–1, columns 3–5. It never leaves row 1, so its queen is locked to that row.
Blue covers 7 squares, spanning 4 rows and 2 columns (rows 1–4, columns 1–2).
Amber occupies 9 squares within rows 1–5, columns 5–8.
Mint: 9 squares across rows 1–6, columns 9–11.
Slate covers 15 squares, spanning 7 rows and 5 columns (rows 2–8, columns 1–5).
Sea green occupies 15 squares within rows 8–11, columns 3–10.
Pale yellow: 16 squares across rows 5–10, columns 6–11.
Red covers 21 squares, spanning 7 rows and 4 columns (rows 2–8, columns 7–10).
Khaki occupies 24 squares within rows 5–11, columns 1–7.
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 1 and 1. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #124.
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 teal 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 #124
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 10 and 11 are the narrowest, touched by only 3 colors. Columns 2 and 11 are the tightest columns, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 10 rows. By contrast row 5 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
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.
Resist the plausible-looking queen. On #124 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 #124 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers five single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 23. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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 10 on this board.
As a sanity check rather than a spoiler: the finished solution to #124 puts 3 queens on the outer border and 8 queens in the interior, 1 of them in an actual corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 #124?
Puzzle #124 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #124 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #124, 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 #124?
Start with the orange region — the most constrained color on this board, with 1 square spanning rows 9–9 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.