11x11 Queens Puzzle #70
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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #70
What follows is a complete solve of puzzle #70, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 11 queen placements and 6 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 rows.
Techniques this board needs: last square in a region, region shadow, region confined to one line, pairing argument on rows, last square in a column.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 2, column 1 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 1, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. The orange region is down to one open square, at row 9, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 11, the remaining orange squares, and the ring of neighbours around row 9, column 11.
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. Wherever blue ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
The board after step 4 — 3 of 11 queens placed. Step 5. Indigo is down to 2 candidates in rows 1 and 4, columns 2 and 3, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about indigo itself.
Step 6. The slate region is down to one open square, at row 5, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 2, the remaining slate squares, and the ring of neighbours around row 5, column 2.
Step 7. 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 8. All of the blue region's remaining squares (2 open squares) lie in column 4. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 9. Only row 10, column 5 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 5, the rest of the sea green region and every square adjacent to it — diagonals included.
The board after step 9 — 6 of 11 queens placed. Step 10. Wherever pale yellow ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 11. Mint is down to 3 candidates in rows 3 and 4, columns 8 and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 12. Here is the pairing argument. The blue and mint regions have no open squares outside rows 3 and 4 — 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: 4 squares come off in one stroke.
Step 13. 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: red has one square left, so its queen takes row 6, column 6; column 7 is down to one square, putting a queen on row 8, column 7; pale yellow has one square left, so its queen takes row 7, column 9; mint has one square left, so its queen takes row 4, column 8; blue has one square left, so its queen takes row 3, 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 3, column 4.
The board after step 13 — 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 #70
Board #70 of the 11x11 bank carries a medium 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, #70 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 #70 are: amber (1 square), orange (1 square), teal (4 squares), indigo (8 squares), blue (9 squares), slate (9 squares), khaki (11 squares), mint (17 squares), pale yellow (18 squares), sea green (19 squares), red (24 squares). An even split would hand every color 11 squares, so the amber region is running 10 squares under that average while the red region is the roomiest area on the grid with 24 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Amber has only 1 place to put its queen; red has 24. The spread between them on this board is 23 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. Amber is the tidiest shape on #70, packing 100% of its 1×1 bounding box, whereas pale yellow straggles across its 8×5 box at just 45%. 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 medium board.
Amber covers 1 square, spanning 1 row and 1 column (rows 2–2, columns 1–1). It never leaves row 2, so its queen is locked to that row.
Orange occupies 1 square within rows 9–9, columns 11–11. It never leaves row 9, so its queen is locked to that row.
Teal: 4 squares across rows 10–11, columns 10–11.
Indigo covers 8 squares, spanning 4 rows and 4 columns (rows 1–4, columns 1–4).
Blue occupies 9 squares within rows 1–4, columns 4–7.
Slate: 9 squares across rows 3–7, columns 1–3.
Khaki covers 11 squares, spanning 5 rows and 3 columns (rows 7–11, columns 6–8).
Mint occupies 17 squares within rows 1–6, columns 8–11.
Pale yellow: 18 squares across rows 4–11, columns 7–11.
Sea green covers 19 squares, spanning 4 rows and 6 columns (rows 8–11, columns 1–6).
Red occupies 24 squares within rows 3–8, columns 2–8.
Where to start on this board
Begin where the choices are fewest. On this board that means amber, which owns just 1 square inside a 1×1 window running from row 2 to row 2 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 never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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.
Work outward to the other flat regions next. Orange 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 #70
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 3 colors. Column 9 is the tightest column, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 4 sits at the far end with 6 colors crossing it; it will almost certainly be among the last to settle.
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.
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 #70 is rated medium
The medium label comes out of four measurable things about #70: four of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 23. Boards that score tight on those measures give up their first queen fast.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
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 #70 the place to look for one is around column 9.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 7 queens in the middle, and nothing in the corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #70?
Puzzle #70 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #70 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #70, 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 #70?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.