11x11 Queens Puzzle #60
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 24-step reasoning is written out below.
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Step-by-step solution for puzzle #60
What follows is a complete solve of puzzle #60, worked the way a person works it rather than the way a computer does. It runs to 24 deductions — 11 queen placements and 13 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: region shadow, region confined to one line, pairing argument on rows, pairing argument on columns, last square in a region, last square in a column.
Show the full walkthrough (19 steps) — contains the solution
Step 1. Wherever mint ends up among its 3 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
Step 2. All of the slate region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 10 squares come off.
Step 3. The indigo region has 4 squares left, spread across rows 1–3, columns 2 and 3. 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 4. Wherever pale yellow 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 5. Mint and slate are now boxed into rows 4 and 5 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 14 squares at once.
The board after step 5 — 0 of 11 queens placed. Step 6. Here is the pairing argument. The indigo, amber, and blue regions have no open squares outside rows 1–3 — 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: 9 squares come off in one stroke.
Step 7. Indigo and pale yellow are now boxed into columns 2 and 3 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 9 squares at once.
Step 8. The mint region is down to one open square, at row 4, column 4. Every colour holds exactly one queen, so that square is forced. Row 4 and column 4 are now spoken for, along with the squares touching that queen.
Step 9. Only row 5, column 1 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 1, the rest of the slate region and every square adjacent to it — diagonals included.
Step 10. All of the red region's remaining squares (2 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
The board after step 10 — 2 of 11 queens placed. Step 11. Orange is down to 3 candidates in rows 8 and 9, columns 6 and 7, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about orange itself.
Step 12. Here is the pairing argument. The blue and orange regions have no open squares outside columns 6 and 7 — 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: 6 squares come off in one stroke.
Step 13. Teal cannot leave row 11 — every one of its open squares (2 open squares) sits there. That row belongs to teal, so every square on it owned by another colour is dead: 6 squares in all.
Step 14. The pale yellow region is down to one open square, at row 7, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 2, the remaining pale yellow squares, and the ring of neighbours around row 7, column 2.
The board after step 14 — 3 of 11 queens placed. Step 15. Only row 1, column 3 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 3, in indigo and in the ring around that square is now dead.
Step 16. The red region is down to one open square, at row 6, column 5. Every colour holds exactly one queen, so that square is forced. Row 6 and column 5 are now spoken for, along with the squares touching that queen.
Step 17. Khaki cannot leave row 8 — every one of its open squares (2 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 5 squares in all.
Step 18. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
Step 19. 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: column 9 is down to one square, putting a queen on row 11, column 9; sea green has one square left, so its queen takes row 10, column 11; khaki has one square left, so its queen takes row 8, column 10; amber has one square left, so its queen takes row 2, column 8; blue has one square left, so its queen takes row 3, column 6; orange has one square left, so its queen takes row 9, column 7. 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 9, column 7.
The board after step 19 — 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 #60
This is puzzle number 60 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.
Like every board on this site, #60 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 #60 are: mint (3 squares), slate (3 squares), teal (6 squares), indigo (8 squares), blue (10 squares), amber (11 squares), pale yellow (11 squares), orange (13 squares), sea green (15 squares), red (20 squares), khaki (21 squares). An even split would hand every color 11 squares, so the mint region is running 8 squares under that average while the khaki region is the roomiest area on the grid with 21 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Mint is working with 3 squares while khaki has 21 to spare, a gap of 18. Attack the cramped end and the roomy regions tend to resolve themselves.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 89% of its 3×3 box, and red the most diffuse at 44% of its 9×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
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.
Mint: 3 squares across rows 4–5, columns 3–4.
Slate covers 3 squares, spanning 2 rows and 2 columns (rows 4–5, columns 1–2).
Teal occupies 6 squares within rows 10–11, columns 6–9.
Indigo: 8 squares across rows 1–3, columns 1–3.
Blue covers 10 squares, spanning 5 rows and 4 columns (rows 1–5, columns 5–8).
Amber occupies 11 squares within rows 1–4, columns 7–11.
Pale yellow: 11 squares across rows 5–11, columns 1–3.
Orange covers 13 squares, spanning 4 rows and 6 columns (rows 8–11, columns 2–7).
Sea green occupies 15 squares within rows 6–11, columns 8–11.
Red: 20 squares across rows 1–9, columns 2–6.
Khaki covers 21 squares, spanning 7 rows and 6 columns (rows 2–8, columns 6–11).
Where to start on this board
Open on the tightest color. Here that is mint, confined to 3 squares between rows 4 and 5 and columns 3 and 4. Its queen has nowhere else to go, which means those 2 rows and 2 columns carry more constraint than anywhere else on #60.
Mint does not collapse onto a single line, so it will not hand you a queen on move one. What it does give you is a short list of 3 candidates. Take each one in turn, imagine the queen there, cross out its row, its column and the eight squares around it, and ask whether any other region is left with nowhere to go. One or two candidates usually fail that test immediately.
Work outward to the other flat regions next. Slate 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 #60
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 6, 7, 9, 10 and 11 are the narrowest, touched by only 4 colors. Columns 1, 4, 5, 10 and 11 are the tightest columns, with 3 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 4 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 5, meeting 6 colors, is the opposite case — the busiest line on #60 and the last one you should expect to crack.
Working through the middle game
The middle of #60 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.
The whole middle game reduces to two sweeps. Sweep the eleven colors looking for one with a single square left; sweep the eleven rows and eleven columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 11x11 solve from a stalled one.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #60 is rated hard
The hard label comes out of four measurable things about #60: it has no region locked to one row or column, its smallest color spans 3 squares, its least crowded row meets 4 colors, and its largest and smallest regions differ by 18. 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 #60 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.
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 column 1 on this board.
Here is a shape check that gives nothing away: when #60 is solved, 4 queens sit on the outer edge of the grid and 7 sit inside it, and no queen lands 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
- 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 #60?
Puzzle #60 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 4 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 11x11 puzzle #60 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #60, 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 #60?
Start with the mint region — the most constrained color on this board, with 3 squares spanning rows 4–5 and columns 3–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.