8x8 Queens Puzzle #50

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 14-step reasoning is written out below.

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Step-by-step solution for puzzle #50

What follows is a complete solve of puzzle #50, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 8 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: region shadow, region confined to one line, pairing argument on rows, last square in a region.

Show the full walkthrough (7 steps) — contains the solution

  1. 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.

  2. Step 2. Mint is down to 3 candidates in rows 4 and 5, columns 5 and 6, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about mint itself.

  3. Step 3. Slate cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 8 squares in all.

  4. Step 4. Wherever blue 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.

    Puzzle #50 after step 4: 0 of 8 queens placed
    The board after step 4 — 0 of 8 queens placed.

  5. Step 5. Mint and slate are now boxed into rows 4 and 5 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 7 squares at once.

  6. Step 6. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.

  7. Step 7. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: amber has one square left, so its queen takes row 2, column 8; indigo has one square left, so its queen takes row 1, column 6; mint has one square left, so its queen takes row 4, column 5; slate has one square left, so its queen takes row 5, column 1; red has one square left, so its queen takes row 6, column 3; blue has one square left, so its queen takes row 3, column 2; khaki has one square left, so its queen takes row 8, column 4; pale yellow has one square left, so its queen takes row 7, 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 7, column 7.

    Puzzle #50 after step 7: 8 of 8 queens placed
    The board after step 7 — 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 #50

Board #50 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.

Like every board on this site, #50 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 #50 are: slate (2 squares), indigo (3 squares), mint (3 squares), blue (6 squares), pale yellow (6 squares), amber (11 squares), khaki (11 squares), red (22 squares). An even split would hand every color 8 squares, so the slate region is running 6 squares under that average while the red region is the roomiest area on the grid with 22 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Slate has only 2 places to put its queen; red has 22. 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.

Look at arrangement as well as area. Slate is the densest region on this grid at 100% of a 2×1 frame; red is the loosest, occupying only 46% of its 8×6 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

Region by region

Here is the full footprint of every color on puzzle #50, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Slate occupies 2 squares within rows 4–5, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.

Indigo: 3 squares across rows 1–2, columns 6–7.

Mint covers 3 squares, spanning 2 rows and 2 columns (rows 4–5, columns 5–6).

Blue occupies 6 squares within rows 2–4, columns 1–3.

Pale yellow: 6 squares across rows 6–8, columns 7–8.

Amber covers 11 squares, spanning 5 rows and 4 columns (rows 1–5, columns 5–8).

Khaki occupies 11 squares within rows 6–8, columns 1–5.

Red: 22 squares across rows 1–8, columns 1–6.

Where to start on this board

Slate is the natural opening on #50: it is the smallest region on the grid at 2 squares, boxed into rows 4–5 and columns 1–1. Since one of those squares must hold a queen, that block of 2 rows and 1 column is the most contested part of the board.

Because slate stays inside column 1, its queen belongs to that column and no other region may use it. Cross out the rest of column 1 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.

Work outward to the other flat regions next. Indigo and mint 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 #50

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3, 6, 7 and 8 are the narrowest, touched by only 3 colors. Columns 4 and 8 are the tightest columns, with 2 colors.

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 4 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

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.

With eight queens to seat and eight regions competing over 64 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 8x8 boards quickly and players who stall halfway.

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 #50 is rated hard

The rating reflects how much the board concedes up front. Puzzle #50 has one region confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 20 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a hard board from the rest.

If #50 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 #50 the place to look for one is around column 4.

As a sanity check rather than a spoiler: the finished solution to #50 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

  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 #50?

Puzzle #50 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.

Does 8x8 puzzle #50 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #50, 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 #50?

Start with the slate region — the most constrained color on this board, with 2 squares spanning rows 4–5 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.