11x11 Queens Puzzle #106
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #106
What follows is a complete solve of puzzle #106, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 11 queen placements and 5 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: last square in a region, region shadow, region confined to one line.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Only row 7, column 2 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 2, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 2. Amber is down to 4 candidates in rows 1–3, columns 6 and 7, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The blue region has 5 squares left, spread across rows 1–4, columns 4 and 5. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
The board after step 3 — 1 of 11 queens placed. Step 4. All of the sea green region's remaining squares (2 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 8 squares come off.
Step 5. Orange cannot leave column 1 — every one of its open squares (3 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 5 squares in all.
Step 6. The indigo region is down to one open square, at row 1, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 4, the remaining indigo squares, and the ring of neighbours around row 1, column 4.
Step 7. Only row 3, column 5 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 5, in blue and in the ring around that square is now dead.
The board after step 7 — 3 of 11 queens placed. Step 8. 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 9. Slate cannot leave column 6 — every one of its open squares (3 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 3 squares in all.
Step 10. 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: teal has one square left, so its queen takes row 11, column 8; sea green has one square left, so its queen takes row 10, column 3; khaki has one square left, so its queen takes row 8, column 9; mint has one square left, so its queen takes row 4, column 10; orange has one square left, so its queen takes row 9, column 1; red has one square left, so its queen takes row 6, column 11; slate has one square left, so its queen takes row 5, 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 5, column 6.
The board after step 10 — 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 #106
Board #106 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.
As with every puzzle in this collection, #106 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 #106 are: pale yellow (1 square), amber (4 squares), blue (6 squares), sea green (6 squares), indigo (12 squares), orange (13 squares), red (14 squares), khaki (14 squares), teal (14 squares), slate (18 squares), mint (19 squares). An even split would hand every color 11 squares, so the pale yellow region is running 10 squares under that average while the mint region is the roomiest area on the grid with 19 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Pale yellow has only 1 place to put its queen; mint has 19. The spread between them on this board is 18 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Square count is only half the story — how a color is arranged counts too. Pale yellow is the tidiest shape on #106, packing 100% of its 1×1 bounding box, whereas khaki straggles across its 6×5 box at just 47%. 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.
Pale yellow covers 1 square, spanning 1 row and 1 column (rows 7–7, columns 2–2). It never leaves row 7, so its queen is locked to that row.
Amber occupies 4 squares within rows 1–3, columns 6–7.
Blue: 6 squares across rows 1–4, columns 4–6.
Sea green covers 6 squares, spanning 4 rows and 2 columns (rows 8–11, columns 2–3).
Indigo occupies 12 squares within rows 1–5, columns 1–4.
Orange: 13 squares across rows 3–11, columns 1–3.
Red covers 14 squares, spanning 7 rows and 3 columns (rows 4–10, columns 9–11).
Khaki occupies 14 squares within rows 6–11, columns 7–11.
Teal: 14 squares across rows 8–11, columns 3–8.
Slate covers 18 squares, spanning 5 rows and 5 columns (rows 4–8, columns 3–7).
Mint occupies 19 squares within rows 1–6, columns 7–11.
Where to start on this board
Begin where the choices are fewest. On this board that means pale yellow, which owns just 1 square inside a 1×1 window running from row 7 to row 7 and column 2 to column 2. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because pale yellow never leaves row 7, its queen must be in that row — and that instantly settles row 7 for everyone else. Sweep along it and X out every square that is not pale yellow. 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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: amber and sea green span 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 #106
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2 and 11 are the narrowest, touched by only 4 colors. Column 1 is the tightest column, with 2 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 8, meeting 6 colors, is the opposite case — the busiest line on #106 and the last one you should expect to crack.
Working through the middle game
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
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 #106 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 #106 is rated hard
The hard label comes out of four measurable things about #106: two of its regions are locked to one row or column, its smallest color spans 1 square, 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.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #106 the place to look for one is around column 1.
Here is a shape check that gives nothing away: when #106 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 #106?
Puzzle #106 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 4 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #106 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #106, 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 #106?
Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 2–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.