11x11 Queens Puzzle #270
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 #270
What follows is a complete solve of puzzle #270, 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 confined to one line.
Techniques this board needs: region confined to one line, last square in a region.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Amber cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 11 squares in all.
Step 2. All of the mint region's remaining squares (4 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 3. Only row 11, column 10 is still open in teal, and since each colour must take a queen, that settles it. Everything else in row 11, in column 10, in teal and in the ring around that square is now dead.
Step 4. The sea green region is down to one open square, at row 10, column 8. Every colour holds exactly one queen, so that square is forced. Row 10 and column 8 are now spoken for, along with the squares touching that queen.
The board after step 4 — 2 of 11 queens placed. Step 5. Only row 9, column 2 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 2, the rest of the orange region and every square adjacent to it — diagonals included.
Step 6. All of the slate region's remaining squares (2 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 7. Only row 3, column 7 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 7, in blue and in the ring around that square is now dead.
The board after step 7 — 4 of 11 queens placed. Step 8. The amber region is down to one open square, at row 2, column 1. Every colour holds exactly one queen, so that square is forced. Row 2 and column 1 are now spoken for, along with the squares touching that queen.
Step 9. Only row 8, column 6 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 6, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 10. All of the indigo region's remaining squares (3 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: mint has one square left, so its queen takes row 4, column 11; slate has one square left, so its queen takes row 5, column 9; pale yellow has one square left, so its queen takes row 7, column 3; red has one square left, so its queen takes row 6, column 5; indigo has one square left, so its queen takes row 1, column 4. 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 1, column 4.
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 #270
Board #270 of the 11x11 bank carries a hard rating. Its 121 squares are shared between eleven colored regions, and the solution places eleven queens: one per row, one per column, one per region, none of them side by side or corner to corner.
Like every board on this site, #270 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 #270 are: amber (2 squares), mint (4 squares), teal (4 squares), orange (8 squares), sea green (9 squares), blue (10 squares), slate (11 squares), indigo (14 squares), red (15 squares), khaki (18 squares), pale yellow (26 squares). An even split would hand every color 11 squares, so the amber region is running 9 squares under that average while the pale yellow region is the roomiest area on the grid with 26 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So amber, with 2 squares, is under far more pressure than pale yellow with 26. A 24-square gap like this one rewards players who start where the choices are fewest.
Square count is only half the story — how a color is arranged counts too. Amber is the tidiest shape on #270, packing 100% of its 2×1 bounding box, whereas khaki straggles across its 6×7 box at just 43%. 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 hard board.
Amber: 2 squares across rows 2–3, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Mint covers 4 squares, spanning 4 rows and 1 column (rows 1–4, columns 11–11). It sits wholly inside column 11, so its queen must be in that column.
Teal occupies 4 squares within rows 9–11, columns 10–11.
Orange: 8 squares across rows 8–11, columns 1–3.
Sea green covers 9 squares, spanning 4 rows and 5 columns (rows 8–11, columns 6–10).
Blue occupies 10 squares within rows 1–4, columns 7–10.
Slate: 11 squares across rows 3–8, columns 8–11.
Indigo covers 14 squares, spanning 3 rows and 7 columns (rows 1–3, columns 1–7).
Red occupies 15 squares within rows 4–8, columns 3–7.
Khaki: 18 squares across rows 6–11, columns 4–10.
Pale yellow covers 26 squares, spanning 8 rows and 6 columns (rows 3–10, columns 1–6).
Where to start on this board
Begin where the choices are fewest. On this board that means amber, which owns just 2 squares inside a 2×1 window running from row 2 to row 3 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because amber 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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: teal spans only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.
The tightest lines on puzzle #270
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 5 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 8 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
The middle of #270 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 #270 is rated hard
The hard label comes out of four measurable things about #270: two of its regions are locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 3 colors, and its largest and smallest regions differ by 24. 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 hard board from the rest.
If #270 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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #270, start hunting for it near row 1.
As a sanity check rather than a spoiler: the finished solution to #270 puts 4 queens on the outer border and 7 queens in the interior, with none in a 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 #270?
Puzzle #270 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #270 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #270, 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 #270?
Start with the amber region — the most constrained color on this board, with 2 squares spanning rows 2–3 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.