8x8 Queens Puzzle #46

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 11-step reasoning is written out below.

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Step-by-step solution for puzzle #46

What follows is a complete solve of puzzle #46, worked the way a person works it rather than the way a computer does. It runs to 11 deductions — 8 queen placements and 3 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 (6 steps) — contains the solution

  1. Step 1. Only row 7, column 1 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 1, the rest of the pale yellow region and every square adjacent to it — diagonals included.

  2. Step 2. The khaki region is down to one open square, at row 8, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 3, the remaining khaki squares, and the ring of neighbours around row 8, column 3.

  3. Step 3. The amber region has 4 squares left, spread across rows 1 and 2, columns 5–7. 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.

    Puzzle #46 after step 3: 2 of 8 queens placed
    The board after step 3 — 2 of 8 queens placed.

  4. Step 4. All of the mint region's remaining squares (2 open squares) lie in row 4. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.

  5. Step 5. Blue cannot leave column 8 — every one of its open squares (3 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 2 squares in all.

  6. Step 6. 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: red has one square left, so its queen takes row 6, column 7; mint has one square left, so its queen takes row 4, column 6; amber has one square left, so its queen takes row 2, column 5; indigo has one square left, so its queen takes row 1, column 2; blue has one square left, so its queen takes row 3, column 8; slate has one square left, so its queen takes row 5, 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 5, column 4.

    Puzzle #46 after step 6: 8 of 8 queens placed
    The board after step 6 — 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 #46

Board #46 of the 8x8 bank carries a medium 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.

Like every board on this site, #46 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.

How the colors divide this board

From smallest to largest, the regions on puzzle #46 are: pale yellow (1 square), mint (2 squares), amber (4 squares), khaki (5 squares), blue (6 squares), indigo (11 squares), red (11 squares), slate (24 squares). An even split would hand every color 8 squares, so the pale yellow region is running 7 squares under that average while the slate 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. Pale yellow has only 1 place to put its queen; slate 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.

Look at arrangement as well as area. Mint is the densest region on this grid at 100% of a 1×2 frame; red is the loosest, occupying only 55% of its 5×4 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.

Pale yellow covers 1 square, spanning 1 row and 1 column (rows 7–7, columns 1–1). It never leaves row 7, so its queen is locked to that row.

Mint occupies 2 squares within rows 4–4, columns 6–7. It never leaves row 4, so its queen is locked to that row.

Amber: 4 squares across rows 1–2, columns 5–7.

Khaki covers 5 squares, spanning 2 rows and 3 columns (rows 7–8, columns 1–3).

Blue occupies 6 squares within rows 1–3, columns 6–8.

Indigo: 11 squares across rows 1–3, columns 1–5.

Red covers 11 squares, spanning 5 rows and 4 columns (rows 4–8, columns 5–8).

Slate occupies 24 squares within rows 3–8, columns 1–6.

Where to start on this board

Pale yellow is the natural opening on #46: it is the smallest region on the grid at 1 square, boxed into rows 7–7 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 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.

Work outward to the other flat regions next. Mint, 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 #46

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5 and 6 are the narrowest, touched by only 2 colors. Columns 4 and 8 are the tightest columns, with 2 colors.

Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 7 rows. Row 7 sits at the far end with 4 colors crossing it; it will almost certainly be among the last to settle.

Working through the middle game

Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.

Keep alternating between two views of the board. In the region view you ask which of the eight 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 8x8 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 #46 is rated medium

Ratings track how generous the opening is. On #46 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 23-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.

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.

If #46 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.

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 #46 the place to look for one is around row 5.

Use this as a rough check on your progress: the completed board has 4 queens around the border and 4 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

  1. The board is an N×N grid divided into N colored regions.
  2. Place exactly one queen (♛) in each row, each column, and each colored region.
  3. No two queens may touch each other — not horizontally, vertically, or diagonally.
  4. 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.
  5. 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 #46?

Puzzle #46 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.

Does 8x8 puzzle #46 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #46, 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 #46?

Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.