8x8 Queens Puzzle #73
Difficulty: medium. 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 10-step reasoning is written out below.
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Step-by-step solution for puzzle #73
What follows is a complete solve of puzzle #73, worked the way a person works it rather than the way a computer does. It runs to 10 deductions — 8 queen placements and 2 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 (4 steps) — contains the solution
Step 1. Only row 1, column 7 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 7, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. Amber is down to 4 candidates in rows 2 and 3, columns 2–4, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
The board after step 2 — 1 of 8 queens placed. Step 3. Blue cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 6 squares in all.
Step 4. 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: pale yellow has one square left, so its queen takes row 7, column 2; slate has one square left, so its queen takes row 5, column 3; amber has one square left, so its queen takes row 2, column 4; blue has one square left, so its queen takes row 3, column 1; khaki has one square left, so its queen takes row 8, column 5; red has one square left, so its queen takes row 6, column 6; mint has one square left, so its queen takes row 4, column 8. 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 4, column 8.
The board after step 4 — 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 #73
Puzzle #73 is one of the medium-rated boards in the 8x8 set. Eight colors divide its 64 squares, and you win by placing eight queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
There is exactly one way to finish #73, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these eight regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #73 are: indigo (1 square), pale yellow (3 squares), blue (5 squares), amber (7 squares), khaki (8 squares), slate (9 squares), red (10 squares), mint (21 squares). An even split would hand every color 8 squares, so the indigo region is running 7 squares under that average while the mint region is the roomiest area on the grid with 21 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; mint has 21. The spread between them on this board is 20 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. Indigo is the tidiest shape on #73, packing 100% of its 1×1 bounding box, whereas mint straggles across its 8×6 box at just 44%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #73 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Indigo covers 1 square, spanning 1 row and 1 column (rows 1–1, columns 7–7). It never leaves row 1, so its queen is locked to that row.
Pale yellow occupies 3 squares within rows 7–8, columns 1–2.
Blue: 5 squares across rows 1–3, columns 1–2.
Amber covers 7 squares, spanning 3 rows and 4 columns (rows 1–3, columns 2–5).
Khaki occupies 8 squares within rows 6–8, columns 2–6.
Slate: 9 squares across rows 4–7, columns 1–3.
Red covers 10 squares, spanning 5 rows and 4 columns (rows 4–8, columns 4–7).
Mint occupies 21 squares within rows 1–8, columns 3–8.
Where to start on this board
Open on the tightest color. Here that is indigo, confined to 1 square between rows 1 and 1 and columns 7 and 7. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #73.
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. Pale yellow 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 #73
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 3, 4 and 5 are the narrowest, touched by only 3 colors. Column 8 is the tightest column, with 1 color.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 7 rows. By contrast row 7 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
The middle of #73 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
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 #73 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 20. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
Stuck on #73 despite the medium rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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 #73 the place to look for one is around column 8.
As a sanity check rather than a spoiler: the finished solution to #73 puts 4 queens on the outer border and 4 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 #73?
Puzzle #73 is rated medium. 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 #73 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #73, 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 #73?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.