8x8 Queens Puzzle #163

Difficulty: easy. 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 #163

What follows is a complete solve of puzzle #163, 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 columns.

Techniques this board needs: region shadow, region confined to one line, pairing argument on rows, pairing argument on columns, last square in a region.

Show the full walkthrough (6 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. All of the slate region's remaining squares (3 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.

  3. Step 3. Red, pale yellow, and khaki are now boxed into rows 6–8 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 9 squares at once.

    Puzzle #163 after step 3: 0 of 8 queens placed
    The board after step 3 — 0 of 8 queens placed.

  4. Step 4. All of the slate 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: 2 squares come off.

  5. Step 5. Indigo and red 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.

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

    Puzzle #163 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 #163

8x8 puzzle #163 is rated easy. Eight colored regions cover its 64 squares, and your job is to seat eight queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.

There is exactly one way to finish #163, 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 #163 are: indigo (3 squares), slate (3 squares), pale yellow (4 squares), red (5 squares), khaki (7 squares), blue (11 squares), amber (14 squares), mint (17 squares). An even split would hand every color 8 squares, so the indigo region is running 5 squares under that average while the mint region is the roomiest area on the grid with 17 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 3 places to put its queen; mint has 17. The spread between them on this board is 14 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

Shape matters as much as size. The slate region is the most compact color here, filling 100% of the 3×1 box that encloses it, while blue is the most scattered at 55% of its 5×4 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.

Region by region

Below is every color on #163 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 3 squares, spanning 2 rows and 2 columns (rows 1–2, columns 7–8).

Slate occupies 3 squares within rows 4–6, columns 5–5. It sits wholly inside column 5, so its queen must be in that column.

Pale yellow: 4 squares across rows 7–8, columns 1–3.

Red covers 5 squares, spanning 3 rows and 2 columns (rows 6–8, columns 7–8).

Khaki occupies 7 squares within rows 5–8, columns 4–6.

Blue: 11 squares across rows 2–6, columns 5–8.

Amber covers 14 squares, spanning 4 rows and 6 columns (rows 1–4, columns 1–6).

Mint occupies 17 squares within rows 2–7, columns 1–4.

Where to start on this board

Begin where the choices are fewest. On this board that means indigo, which owns just 3 squares inside a 2×2 window running from row 1 to row 2 and column 7 to column 8. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

Indigo spans 2 rows, so it stays open for now — but it is still the shortest list on the board at 3 squares. Work through those squares first and mark the ones that would leave another region homeless. That pruning is what makes the rest of the grid legible.

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 #163

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

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 #163 is rated easy

What earns a board its rating is the shape of its opening. Here that opening offers one single-line region, a 3-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 14. 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 #163 despite the easy 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 #163 the place to look for one is around row 1.

Use this as a rough check on your progress: the completed board has 3 queens around the border and 5 queens in the middle, including 1 in a corner. 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 #163?

Puzzle #163 is rated easy. Its smallest color region holds 3 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.

Does 8x8 puzzle #163 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #163, 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 #163?

Start with the indigo region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 7–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.