11x11 Queens Puzzle #74
Difficulty: easy. 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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #74
What follows is a complete solve of puzzle #74, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 11 queen placements and 10 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, pairing argument on rows, pairing argument on columns, region confined to one line, line confined to one region, last square in a row, last square in a column, last square in a region.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Wherever indigo ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 2. Teal is down to 3 candidates in rows 10 and 11, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about teal itself.
Step 3. Khaki, orange, sea green, and teal are now boxed into rows 8–11 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 13 squares at once.
Step 4. Wherever red ends up among its 3 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 — 0 of 11 queens placed. Step 5. Indigo and teal are now boxed into columns 1 and 2 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 6. Here is the pairing argument. The amber and red regions have no open squares outside columns 10 and 11 — 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: 11 squares come off in one stroke.
Step 7. 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: 10 squares in all.
Step 8. Sea green is down to 3 candidates in rows 10 and 11, columns 7 and 8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about sea green itself.
The board after step 8 — 0 of 11 queens placed. Step 9. Row 9 has only orange squares left (2 open squares). The row needs a queen and only orange can provide one, which pins that colour to this row and kills its squares elsewhere: 9 squares.
Step 10. 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: row 8 is down to one square, putting a queen on row 8, column 9; column 10 is down to one square, putting a queen on row 2, column 10; indigo has one square left, so its queen takes row 1, column 1; teal has one square left, so its queen takes row 11, column 2; sea green has one square left, so its queen takes row 10, column 8; orange has one square left, so its queen takes row 9, 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 9, column 6.
Step 11. All of the slate region's remaining squares (3 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
Step 12. 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 5; row 4 is down to one square, putting a queen on row 4, column 3; pale yellow has one square left, so its queen takes row 7, column 4; 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 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 5, column 7.
The board after step 12 — 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 #74
Board #74 of the 11x11 bank carries a easy 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, #74 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 #74 are: indigo (3 squares), teal (3 squares), red (4 squares), amber (6 squares), khaki (7 squares), sea green (8 squares), orange (12 squares), slate (13 squares), pale yellow (20 squares), blue (21 squares), mint (24 squares). An even split would hand every color 11 squares, so the indigo region is running 8 squares under that average while the mint region is the roomiest area on the grid with 24 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 indigo, with 3 squares, is under far more pressure than mint with 24. A 21-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Slate is the densest region on this grid at 81% of a 4×4 frame; orange is the loosest, occupying only 50% of its 4×6 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Indigo occupies 3 squares within rows 1–2, columns 1–2.
Teal: 3 squares across rows 10–11, columns 1–2.
Red covers 4 squares, spanning 3 rows and 2 columns (rows 6–8, columns 10–11).
Amber occupies 6 squares within rows 1–5, columns 10–11.
Khaki: 7 squares across rows 8–10, columns 9–11.
Sea green covers 8 squares, spanning 3 rows and 5 columns (rows 9–11, columns 7–11).
Orange occupies 12 squares within rows 8–11, columns 3–8.
Slate: 13 squares across rows 4–7, columns 7–10.
Pale yellow covers 20 squares, spanning 6 rows and 6 columns (rows 5–10, columns 1–6).
Blue occupies 21 squares within rows 1–4, columns 4–10.
Mint: 24 squares across rows 1–7, columns 1–6.
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 3 squares inside a 2×2 window running from row 1 to row 2 and column 1 to column 2. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
With 2 rows and 2 columns of room, indigo needs narrowing rather than solving outright. Test its 3 squares against the neighbours: a candidate that would strand another color is dead, and eliminating even two of them tightens the whole corner of the board around rows 1–2.
Work outward to the other flat regions next. Teal is no more than two rows tall, so its queen is 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 #74
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3 and 11 are the narrowest, touched by only 3 colors. Column 3 is the tightest column, with 3 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 10 sits at the far end with 5 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.
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 #74 is rated easy
Ratings track how generous the opening is. On #74 you get no region pinned to a single row or column, a smallest color of 3 squares, a tightest row crossed by 3 colors, and a 21-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.
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.
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 #74, start hunting for it near row 3.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 8 queens in the middle, including 1 in a corner. 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 #74?
Puzzle #74 is rated easy. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 11x11 puzzle #74 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #74, 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 #74?
Start with the indigo region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.