8x8 Queens Puzzle #155

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 19-step reasoning is written out below.

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Step-by-step solution for puzzle #155

What follows is a complete solve of puzzle #155, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 8 queen placements and 11 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 confined to one line, region shadow, pairing argument on columns, pairing argument on rows, last square in a region.

Show the full walkthrough (12 steps) — contains the solution

  1. Step 1. Red cannot leave column 8 — every one of its open squares (3 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 6 squares in all.

  2. Step 2. Amber is down to 4 candidates in rows 2, 4, and 5, columns 6 and 7, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.

  3. Step 3. The khaki region has 4 squares left, spread across rows 7 and 8, columns 5–7. 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.

  4. Step 4. Here is the pairing argument. The amber, blue, and khaki regions have no open squares outside columns 5–7 — 3 colours confined to 3 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 7 squares come off in one stroke.

    Puzzle #155 after step 4: 0 of 8 queens placed
    The board after step 4 — 0 of 8 queens placed.

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

  6. Step 6. Here is the pairing argument. The pale yellow and khaki regions have no open squares outside rows 7 and 8 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 3 squares come off in one stroke.

  7. Step 7. Red cannot leave column 8 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 1 square in all.

  8. Step 8. Here is the pairing argument. The slate and red regions have no open squares outside rows 5 and 6 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 4 squares come off in one stroke.

    Puzzle #155 after step 8: 0 of 8 queens placed
    The board after step 8 — 0 of 8 queens placed.

  9. Step 9. Mint cannot leave row 4 — every one of its open squares (3 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 4 squares in all.

  10. Step 10. All of the amber region's remaining squares (2 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.

  11. Step 11. Blue cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 2 squares in all.

  12. Step 12. 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 7; khaki has one square left, so its queen takes row 8, column 6; pale yellow has one square left, so its queen takes row 7, column 3; slate has one square left, so its queen takes row 5, column 4; mint has one square left, so its queen takes row 4, column 2; indigo has one square left, so its queen takes row 1, column 1; blue has one square left, so its queen takes row 3, column 5; red has one square left, so its queen takes row 6, 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 6, column 8.

    Puzzle #155 after step 12: 8 of 8 queens placed
    The board after step 12 — 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 #155

8x8 puzzle #155 is rated medium. 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 #155, 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 #155 are: red (3 squares), blue (6 squares), khaki (6 squares), amber (8 squares), slate (9 squares), pale yellow (9 squares), mint (10 squares), indigo (13 squares). An even split would hand every color 8 squares, so the red region is running 5 squares under that average while the indigo region is the roomiest area on the grid with 13 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Red has only 3 places to put its queen; indigo has 13. The spread between them on this board is 10 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 red region is the most compact color here, filling 100% of the 3×1 box that encloses it, while slate is the most scattered at 45% of its 4×5 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

Here is the full footprint of every color on puzzle #155, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Red occupies 3 squares within rows 5–7, columns 8–8. It sits wholly inside column 8, so its queen must be in that column.

Blue: 6 squares across rows 1–4, columns 5–7.

Khaki covers 6 squares, spanning 3 rows and 4 columns (rows 6–8, columns 5–8).

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

Slate: 9 squares across rows 3–6, columns 3–7.

Pale yellow covers 9 squares, spanning 3 rows and 6 columns (rows 6–8, columns 1–6).

Mint occupies 10 squares within rows 4–7, columns 1–4.

Indigo: 13 squares across rows 1–4, columns 1–4.

Where to start on this board

Begin where the choices are fewest. On this board that means red, which owns just 3 squares inside a 3×1 window running from row 5 to row 7 and column 8 to column 8. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

Because red stays inside column 8, its queen belongs to that column and no other region may use it. Cross out the rest of column 8 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.

Nothing on this grid is pinned to one or two lines, which is why the opening takes patience. Scan the columns for one where only two or three colors appear — whichever region is forced into it claims that column outright. Chaining two of those observations is normally enough to break #155 open.

The tightest lines on puzzle #155

A quick way to find the next move is to count how many different colors touch each line. On this board, row 8 is the narrowest, touched by only 2 colors. Columns 1, 2 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

After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.

Two checks, run alternately, will carry you through the 64 squares of this grid. First: has any of the eight regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 8x8 boards almost always run one of those checks and forget the other.

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 #155 is rated medium

The rating reflects how much the board concedes up front. Puzzle #155 has one region confined to a single row or column, its smallest color holds 3 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 10 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

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 #155 despite the medium 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 #155 the place to look for one is around row 8.

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 #155?

Puzzle #155 is rated medium. 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 #155 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #155, 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 #155?

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