8x8 Queens Puzzle #134

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 12-step reasoning is written out below.

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Step-by-step solution for puzzle #134

What follows is a complete solve of puzzle #134, worked the way a person works it rather than the way a computer does. It runs to 12 deductions — 8 queen placements and 4 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: region shadow, pairing argument on columns, last square in a region.

Show the full walkthrough (8 steps) — contains the solution

  1. Step 1. Wherever blue ends up among its 7 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.

  2. Step 2. Slate is down to 3 candidates in rows 4 and 5, columns 7 and 8, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about slate itself.

  3. Step 3. Slate and pale yellow are now boxed into columns 7 and 8 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 6 squares at once.

  4. Step 4. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: 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 7; 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 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 7, column 8.

    Puzzle #134 after step 4: 5 of 8 queens placed
    The board after step 4 — 5 of 8 queens placed.

  5. Step 5. The amber region has 4 squares left, spread across rows 2 and 3, columns 1–3. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.

  6. Step 6. The blue region is down to one open square, at row 3, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 3, the remaining blue squares, and the ring of neighbours around row 3, column 3.

  7. Step 7. Only row 2, column 1 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 1, in amber and in the ring around that square is now dead.

  8. Step 8. The red region is down to one open square, at row 6, column 2. Every colour holds exactly one queen, so that square is forced. Row 6 and column 2 are now spoken for, along with the squares touching that queen.

    Puzzle #134 after step 8: 8 of 8 queens placed
    The board after step 8 — 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 #134

Board #134 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, #134 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 #134 are: slate (3 squares), khaki (5 squares), indigo (6 squares), pale yellow (6 squares), blue (7 squares), mint (7 squares), amber (9 squares), red (21 squares). An even split would hand every color 8 squares, so the slate region is running 5 squares under that average while the red 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. Slate has only 3 places to put its queen; red has 21. 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.

Look at arrangement as well as area. Khaki is the densest region on this grid at 83% of a 2×3 frame; blue is the loosest, occupying only 44% of its 4×4 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.

Slate occupies 3 squares within rows 4–5, columns 7–8.

Khaki: 5 squares across rows 7–8, columns 4–6.

Indigo covers 6 squares, spanning 3 rows and 3 columns (rows 1–3, columns 6–8).

Pale yellow occupies 6 squares within rows 5–8, columns 7–8.

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

Mint covers 7 squares, spanning 4 rows and 3 columns (rows 2–5, columns 5–7).

Amber occupies 9 squares within rows 1–4, columns 1–4.

Red: 21 squares across rows 4–8, columns 1–7.

Where to start on this board

Slate is the natural opening on #134: it is the smallest region on the grid at 3 squares, boxed into rows 4–5 and columns 7–8. Since one of those squares must hold a queen, that block of 2 rows and 2 columns is the most contested part of the board.

With 2 rows and 2 columns of room, slate needs narrowing rather than solving outright. Test its 3 squares against the neighbours: a candidate that would strand another color is dead, and eliminating even two of them tightens the whole corner of the board around rows 4–5.

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 #134

A quick way to find the next move is to count how many different colors touch each line. On this board, row 6 is the narrowest, touched by only 2 colors. Column 1 is the tightest column, with 2 colors.

A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 7 rows. Row 4 is the crowded extreme at 5 colors — worth revisiting later, not now.

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.

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.

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 #134 is rated hard

Ratings track how generous the opening is. On #134 you get no region pinned to a single row or column, a smallest color of 3 squares, a tightest row crossed by 2 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 #134 the place to look for one is around row 6.

A non-spoiling distribution check: solved, #134 carries 4 queens on the perimeter against 4 queens inside, with the corners empty. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.

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 #134?

Puzzle #134 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 2 colors, and no region is confined to a single row or column, so the opening move takes some hunting.

Does 8x8 puzzle #134 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #134, 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 #134?

Start with the slate region — the most constrained color on this board, with 3 squares spanning rows 4–5 and columns 7–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.