8x8 Queens Puzzle #118
Difficulty: hard. Place 8 queens on this 8x8 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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #118
What follows is a complete solve of puzzle #118, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 8 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: last square in a region, region confined to one line, region shadow, pairing argument on rows, pairing argument on columns, last square in a column, line confined to one region, last square in a row.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 1, column 1 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 1, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. All of the amber region's remaining squares (2 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 3. 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: 5 squares in all.
Step 4. All of the mint region's remaining squares (2 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
The board after step 4 — 1 of 8 queens placed. Step 5. Khaki is down to 4 candidates in rows 7 and 8, columns 5–7, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about khaki itself.
Step 6. Here is the pairing argument. The pale yellow and khaki regions have no open squares outside rows 7 and 8 — 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: 2 squares come off in one stroke.
Step 7. Wherever red 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 8. Here is the pairing argument. The amber and red regions have no open squares outside columns 7 and 8 — 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: 3 squares come off in one stroke.
Step 9. 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: 2 squares in all.
The board after step 9 — 1 of 8 queens placed. Step 10. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
Step 11. Scan column 3 and only row 7, column 3 remains — a pale yellow square. Every column takes a queen, so it takes this one. Cross out the whole of row 7 and column 3, the remaining pale yellow squares, and the ring of neighbours around row 7, column 3.
Step 12. Every open square left in column 4 (2 open squares) belongs to the slate region. Since that column must contain a queen, slate is the colour that supplies it — so slate squares anywhere else on the board are out, 4 squares in all.
Step 13. 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 6 is down to one square, putting a queen on row 6, column 8; amber has one square left, so its queen takes row 2, column 7; blue has one square left, so its queen takes row 3, column 5; slate has one square left, so its queen takes row 5, column 4; mint has one square left, so its queen takes row 4, column 2; khaki has one square left, so its queen takes row 8, 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 8, column 6.
The board after step 13 — 8 of 8 queens placed.
That completes the board: 8 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 8x8 Queens puzzle #118
Board #118 of the 8x8 bank carries a hard rating. Its 64 squares are shared between eight colored regions, and the solution places eight 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, #118 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 #118 are: indigo (1 square), khaki (4 squares), amber (6 squares), mint (7 squares), red (7 squares), pale yellow (9 squares), blue (11 squares), slate (19 squares). An even split would hand every color 8 squares, so the indigo region is running 7 squares under that average while the slate 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. Indigo has only 1 place to put its queen; slate 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.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and red the most diffuse at 58% of its 6×2 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
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 covers 1 square, spanning 1 row and 1 column (rows 1–1, columns 1–1). It never leaves row 1, so its queen is locked to that row.
Khaki occupies 4 squares within rows 7–8, columns 5–7.
Amber: 6 squares across rows 1–2, columns 5–8.
Mint covers 7 squares, spanning 4 rows and 2 columns (rows 2–5, columns 1–2).
Red occupies 7 squares within rows 3–8, columns 7–8.
Pale yellow: 9 squares across rows 6–8, columns 1–4.
Blue covers 11 squares, spanning 3 rows and 6 columns (rows 1–3, columns 2–7).
Slate occupies 19 squares within rows 3–7, columns 2–7.
Where to start on this board
Indigo is the natural opening on #118: it is the smallest region on the grid at 1 square, boxed into rows 1–1 and columns 1–1. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Amber and khaki 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 #118
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 4, 5, 6 and 8 are the narrowest, touched by only 3 colors. Column 8 is the tightest column, with 2 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 7 rows. Row 7, meeting 4 colors, is the opposite case — the busiest line on #118 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.
The whole middle game reduces to two sweeps. Sweep the eight colors looking for one with a single square left; sweep the eight rows and eight columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 8x8 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 #118 is rated hard
Ratings track how generous the opening is. On #118 you get two regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 18-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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 8x8
At 8x8 the whole grid stays within a single glance, which makes systematic scanning practical. Read the rows in order and count the colors in each — a row touched by two colors is far more constrained than one touched by five, and that is usually where the next forced move hides. The board is small enough that re-scanning from the top after each placement costs almost nothing.
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 #118 the place to look for one is around column 8.
Here is a shape check that gives nothing away: when #118 is solved, 3 queens sit on the outer edge of the grid and 5 sit inside it, with 1 queen 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 8x8 Queens puzzle #118?
Puzzle #118 is rated hard. Its smallest color region holds 1 square, 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 8x8 puzzle #118 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #118, has been verified to have exactly one valid arrangement of eight queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #118?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.