8x8 Queens Puzzle #125

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 13-step reasoning is written out below.

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Step-by-step solution for puzzle #125

What follows is a complete solve of puzzle #125, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 8 queen placements and 5 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: last square in a region, region shadow, region confined to one line, pairing argument on rows.

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

  1. Step 1. Only row 5, column 8 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 8, the rest of the slate region and every square adjacent to it — diagonals included.

  2. Step 2. Blue is down to 4 candidates in rows 1–4, columns 6 and 7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.

  3. Step 3. The mint region has 2 squares left, spread across rows 4 and 6, columns 1 and 2. You do not need to know which of them takes the queen: every one of those options attacks the same 4 squares, so they can be crossed out now.

  4. Step 4. All of the khaki region's remaining squares (2 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 9 squares come off.

    Puzzle #125 after step 4: 1 of 8 queens placed
    The board after step 4 — 1 of 8 queens placed.

  5. Step 5. Mint, red, pale yellow, and khaki are now boxed into rows 4, 6, 7, and 8 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 1 square at once.

  6. Step 6. All of the blue 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.

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

    Puzzle #125 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 #125

Puzzle #125 is one of the hard-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 #125, 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 #125 are: slate (1 square), khaki (2 squares), mint (4 squares), indigo (7 squares), blue (9 squares), amber (12 squares), pale yellow (14 squares), red (15 squares). An even split would hand every color 8 squares, so the slate region is running 7 squares under that average while the red region is the roomiest area on the grid with 15 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 slate, with 1 square, is under far more pressure than red with 15. A 14-square gap like this one rewards players who start where the choices are fewest.

Square count is only half the story — how a color is arranged counts too. Slate is the tidiest shape on #125, packing 100% of its 1×1 bounding box, whereas red straggles across its 5×5 box at just 60%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Here is the full footprint of every color on puzzle #125, 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 1 square within rows 5–5, columns 8–8. It never leaves row 5, so its queen is locked to that row.

Khaki: 2 squares across rows 7–8, columns 5–5. It sits wholly inside column 5, so its queen must be in that column.

Mint covers 4 squares, spanning 3 rows and 2 columns (rows 4–6, columns 1–2).

Indigo occupies 7 squares within rows 1–3, columns 4–6.

Blue: 9 squares across rows 1–4, columns 6–8.

Amber covers 12 squares, spanning 4 rows and 4 columns (rows 1–4, columns 1–4).

Pale yellow occupies 14 squares within rows 4–8, columns 1–4.

Red: 15 squares across rows 4–8, columns 4–8.

Where to start on this board

Open on the tightest color. Here that is slate, confined to 1 square between rows 5 and 5 and columns 8 and 8. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #125.

Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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. Khaki 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 #125

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3, 6, 7 and 8 are the narrowest, touched by only 3 colors. Columns 3 and 7 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 3 colors, so one of that handful must take the row and the rest are squeezed into the other 7 rows. Row 4 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

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.

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 #125 is rated hard

The rating reflects how much the board concedes up front. Puzzle #125 has three regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 14 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

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.

Stuck on #125 despite the hard 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.

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 #125, start hunting for it near column 3.

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 #125?

Puzzle #125 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.

Does 8x8 puzzle #125 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #125, 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 #125?

Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.