11x11 Queens Puzzle #68
Difficulty: medium. 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 #68
What follows is a complete solve of puzzle #68, 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 region shadow.
Techniques this board needs: region confined to one line, region shadow, last square in a region, last square in a row.
Show the full walkthrough (16 steps) — contains the solution
Step 1. Amber cannot leave row 2 — every one of its open squares (4 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 7 squares in all.
Step 2. All of the indigo region's remaining squares (6 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 3. The blue region has 4 squares left, spread across rows 3 and 4, columns 1–3. 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. All of the orange region's remaining squares (3 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 5. Blue cannot leave row 3 — every one of its open squares (2 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 9 squares in all.
The board after step 5 — 0 of 11 queens placed. Step 6. The mint region is down to one open square, at row 4, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 11, the remaining mint squares, and the ring of neighbours around row 4, column 11.
Step 7. Sea green cannot leave column 10 — every one of its open squares (2 open squares) sits there. That column belongs to sea green, so every square in it owned by another colour is dead: 8 squares in all.
Step 8. The teal region is down to one open square, at row 11, column 8. Every colour holds exactly one queen, so that square is forced. Row 11 and column 8 are now spoken for, along with the squares touching that queen.
Step 9. Only row 10, column 10 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 10, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 10. The orange region is down to one open square, at row 9, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 1, the remaining orange squares, and the ring of neighbours around row 9, column 1.
Step 11. Khaki cannot leave column 9 — every one of its open squares (2 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 4 squares in all.
The board after step 11 — 4 of 11 queens placed. Step 12. The amber region is down to one open square, at row 2, column 7. Every colour holds exactly one queen, so that square is forced. Row 2 and column 7 are now spoken for, along with the squares touching that queen.
Step 13. Only row 1, column 5 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 5, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 14. All of the red region's remaining squares (2 open squares) lie in column 6. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
Step 15. Pale yellow cannot leave column 3 — 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: 6 squares in all.
Step 16. 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: blue has one square left, so its queen takes row 3, column 2; row 7 is down to one square, putting a queen on row 7, column 3; slate has one square left, so its queen takes row 5, column 4; red has one square left, so its queen takes row 6, column 6; khaki has one square left, so its queen takes row 8, column 9. 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 8, column 9.
The board after step 16 — 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 #68
This is puzzle number 68 in the 11x11 collection, rated medium. 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, #68 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 #68 are: orange (3 squares), teal (3 squares), amber (4 squares), sea green (5 squares), indigo (7 squares), mint (7 squares), blue (11 squares), red (18 squares), slate (21 squares), pale yellow (21 squares), khaki (21 squares). An even split would hand every color 11 squares, so the orange 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. Orange 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 amber is the most solid, filling 100% of its 1×4 box, and khaki the most diffuse at 44% of its 8×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Here is the full footprint of every color on puzzle #68, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Orange occupies 3 squares within rows 9–11, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Teal: 3 squares across rows 10–11, columns 8–9.
Amber covers 4 squares, spanning 1 row and 4 columns (rows 2–2, columns 7–10). It never leaves row 2, so its queen is locked to that row.
Sea green occupies 5 squares within rows 9–11, columns 10–11.
Indigo: 7 squares across rows 1–2, columns 5–10.
Mint covers 7 squares, spanning 4 rows and 4 columns (rows 1–4, columns 8–11).
Blue occupies 11 squares within rows 1–4, columns 1–4.
Red: 18 squares across rows 3–8, columns 5–9.
Slate covers 21 squares, spanning 7 rows and 5 columns (rows 2–8, columns 1–5).
Pale yellow occupies 21 squares within rows 7–11, columns 1–7.
Khaki: 21 squares across rows 4–11, columns 6–11.
Where to start on this board
Open on the tightest color. Here that is orange, confined to 3 squares between rows 9 and 11 and columns 1 and 1. Its queen has nowhere else to go, which means those 3 rows and 1 column carry more constraint than anywhere else on #68.
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, 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 #68
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 5 and 6 are the narrowest, touched by only 3 colors. Columns 2, 3, 4 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 3 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 11, meeting 5 colors, is the opposite case — the busiest line on #68 and the last one you should expect to crack.
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.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #68 is rated medium
The rating reflects how much the board concedes up front. Puzzle #68 has two regions confined to a single row or column, its smallest color holds 3 squares, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 18 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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 medium board from the rest.
If #68 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 row 1 on this board.
Here is a shape check that gives nothing away: when #68 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 #68?
Puzzle #68 is rated medium. Its smallest color region holds 3 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 #68 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #68, 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 #68?
Start with the orange region — the most constrained color on this board, with 3 squares spanning rows 9–11 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.