11x11 Queens Puzzle #5
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 29-step reasoning is written out below.
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Step-by-step solution for puzzle #5
What follows is a complete solve of puzzle #5, worked the way a person works it rather than the way a computer does. It runs to 29 deductions — 11 queen placements and 18 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: region confined to one line, region shadow, last square in a region, line confined to one region, pairing argument on rows, pairing argument on columns, proof by contradiction, last square in a row.
Show the full walkthrough (22 steps) — contains the solution
Step 1. Amber cannot leave row 2 — every one of its open squares (3 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 10 squares in all.
Step 2. Blue is down to 7 candidates in rows 3–5, columns 6–9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 3. Orange cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 10 squares in all.
Step 4. Wherever sea green ends up among its 2 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
Step 5. 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 6. The teal region has 3 squares left, spread across rows 10 and 11, 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.
The board after step 6 — 1 of 11 queens placed. Step 7. Row 1 has only indigo squares left (9 open squares). The row needs a queen and only indigo can provide one, which pins that colour to this row and kills its squares elsewhere: 10 squares.
Step 8. Here is the pairing argument. The sea green and teal regions have no open squares outside rows 10 and 11 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 11 squares come off in one stroke.
Step 9. Khaki cannot leave row 8 — every one of its open squares (3 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 6 squares in all.
Step 10. 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.
Step 11. Slate is down to 3 candidates in rows 5 and 6, columns 2 and 3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
The board after step 11 — 1 of 11 queens placed. Step 12. Here is the pairing argument. The mint and teal regions have no open squares outside columns 4 and 5 — 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: 3 squares come off in one stroke.
Step 13. Only row 7, column 6 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 6, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 14. Here is the pairing argument. The slate 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: 2 squares come off in one stroke.
Step 15. Test row 1, column 8 for indigo: place a queen there, run the forced consequences through, and row 3 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 16. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 9. Follow the forced moves that would create and row 3 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 17. Test row 1, column 11 for indigo: place a queen there, run the forced consequences through, and row 3 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
The board after step 17 — 2 of 11 queens placed. Step 18. The indigo region is down to one open square, at row 1, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 7, the remaining indigo squares, and the ring of neighbours around row 1, column 7.
Step 19. Wherever blue ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 20. Now a short proof by contradiction. Suppose the amber queen went to row 2, column 9. Follow the forced moves that would create and row 3 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 21. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 1 square in all.
Step 22. 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: row 3 is down to one square, putting a queen on row 3, column 8; khaki has one square left, so its queen takes row 8, column 11; amber has one square left, so its queen takes row 2, column 10; red has one square left, so its queen takes row 6, column 9; slate has one square left, so its queen takes row 5, column 2; mint has one square left, so its queen takes row 4, column 4; sea green has one square left, so its queen takes row 10, column 3; teal has one square left, so its queen takes row 11, column 5. 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 11, column 5.
The board after step 22 — 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 #5
Puzzle #5 is one of the easy-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.
Like every board on this site, #5 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 #5 are: orange (2 squares), amber (3 squares), sea green (5 squares), mint (6 squares), teal (6 squares), blue (9 squares), pale yellow (12 squares), khaki (13 squares), slate (16 squares), red (21 squares), indigo (28 squares). An even split would hand every color 11 squares, so the orange region is running 9 squares under that average while the indigo region is the roomiest area on the grid with 28 squares.
Every color takes one queen and one only, whatever its size — which is why the 26 square difference between orange and indigo 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 1×3 box that encloses it, while sea green is the most scattered at 56% of its 3×3 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.
Orange occupies 2 squares within rows 9–10, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Amber: 3 squares across rows 2–2, columns 9–11. It never leaves row 2, so its queen is locked to that row.
Sea green covers 5 squares, spanning 3 rows and 3 columns (rows 9–11, columns 1–3).
Mint occupies 6 squares within rows 4–6, columns 3–5.
Teal: 6 squares across rows 9–11, columns 3–5.
Blue covers 9 squares, spanning 4 rows and 4 columns (rows 2–5, columns 6–9).
Pale yellow occupies 12 squares within rows 7–11, columns 5–8.
Khaki: 13 squares across rows 8–11, columns 7–11.
Slate covers 16 squares, spanning 6 rows and 4 columns (rows 4–9, columns 1–4).
Red occupies 21 squares within rows 3–8, columns 6–11.
Indigo: 28 squares across rows 1–4, columns 1–11.
Where to start on this board
Orange is the natural opening on #5: it is the smallest region on the grid at 2 squares, boxed into rows 9–10 and columns 1–1. Since one of those squares must hold a queen, that block of 2 rows and 1 column is the most contested part of the board.
Because orange stays inside column 1, its queen belongs to that column and no other region may use it. Cross out the rest of column 1 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
Work outward to the other flat regions next. Amber 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 #5
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 1 color. Column 2 is the tightest column, with 3 colors.
A line with few colors is a line close to resolving. Where only 1 color appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 9 is the crowded extreme at 6 colors — worth revisiting later, not now.
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.
Keep alternating between two views of the board. In the region view you ask which of the eleven colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 11x11 board unwinds.
Resist the plausible-looking queen. On #5 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 #5 is rated easy
Ratings track how generous the opening is. On #5 you get two regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 1 color, and a 26-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
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.
If #5 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.
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 #5 is row 1.
A non-spoiling distribution check: solved, #5 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
- 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 #5?
Puzzle #5 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 1 color, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #5 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #5, 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 #5?
Start with the orange region — the most constrained color on this board, with 2 squares spanning rows 9–10 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.