8x8 Queens Puzzle #124
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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #124
What follows is a complete solve of puzzle #124, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 8 queen placements and 12 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, last square in a column.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Wherever indigo ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. All of the blue region's remaining squares (3 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 3. The mint region has 3 squares left, spread across rows 3 and 4, columns 1 and 2. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 4. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 5. Amber is down to 4 candidates in rows 2 and 3, columns 3–5, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
The board after step 5 — 0 of 8 queens placed. Step 6. All of the blue region's remaining squares (2 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.
Step 7. Wherever pale yellow ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 8. Khaki is down to 4 candidates in rows 6 and 8, columns 5–7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about khaki itself.
Step 9. The pale yellow region has 3 squares left, spread across rows 6 and 7, columns 4–6. 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.
Step 10. Here is the pairing argument. The amber and blue regions have no open squares outside rows 2 and 3 — 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.
The board after step 10 — 0 of 8 queens placed. Step 11. Only row 4, column 1 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 1, in mint and in the ring around that square is now dead.
Step 12. The indigo region is down to one open square, at row 1, column 2. Every colour holds exactly one queen, so that square is forced. Row 1 and column 2 are now spoken for, along with the squares touching that queen.
Step 13. Slate cannot leave row 5 — every one of its open squares (3 open squares) sits there. That row belongs to slate, so every square on it owned by another colour is dead: 3 squares in all.
Step 14. Red is down to 4 candidates in rows 6–8, columns 3 and 4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.
Step 15. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: pale yellow has one square left, so its queen takes row 7, column 5; amber has one square left, so its queen takes row 2, column 4; blue has one square left, so its queen takes row 3, column 8; column 6 is down to one square, putting a queen on row 5, column 6; khaki has one square left, so its queen takes row 8, column 7; red has one square left, so its queen takes row 6, 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 6, column 3.
The board after step 15 — 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 #124
This is puzzle number 124 in the 8x8 collection, rated hard. The grid holds 64 squares split between eight colored regions, and a finished board carries eight queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
As with every puzzle in this collection, #124 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 #124 are: indigo (3 squares), blue (3 squares), mint (4 squares), pale yellow (4 squares), khaki (7 squares), amber (8 squares), slate (15 squares), red (20 squares). An even split would hand every color 8 squares, so the indigo region is running 5 squares under that average while the red region is the roomiest area on the grid with 20 squares.
Every color takes one queen and one only, whatever its size — which is why the 17 square difference between indigo and red is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Shape matters as much as size. The blue region is the most compact color here, filling 100% of the 3×1 box that encloses it, while slate is the most scattered at 50% of its 6×5 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
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a hard board.
Indigo covers 3 squares, spanning 2 rows and 2 columns (rows 1–2, columns 1–2).
Blue occupies 3 squares within rows 1–3, columns 8–8. It sits wholly inside column 8, so its queen must be in that column.
Mint: 4 squares across rows 2–4, columns 1–2.
Pale yellow covers 4 squares, spanning 2 rows and 3 columns (rows 6–7, columns 4–6).
Khaki occupies 7 squares within rows 6–8, columns 5–8.
Amber: 8 squares across rows 1–3, columns 3–6.
Slate covers 15 squares, spanning 6 rows and 5 columns (rows 1–6, columns 4–8).
Red occupies 20 squares within rows 3–8, columns 1–5.
Where to start on this board
The most constrained color is where a solve should begin, and on #124 that is indigo with 3 squares. It reaches from row 1 to row 2 and from column 1 to column 2 — 2 rows by 2 columns. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Indigo does not collapse onto a single line, so it will not hand you a queen on move one. What it does give you is a short list of 3 candidates. Take each one in turn, imagine the queen there, cross out its row, its column and the eight squares around it, and ask whether any other region is left with nowhere to go. One or two candidates usually fail that test immediately.
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 #124
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5 and 8 are the narrowest, touched by only 2 colors. Columns 3 and 7 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 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 7 rows. By contrast row 3 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
The middle of #124 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
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.
Resist the plausible-looking queen. On #124 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #124 is rated hard
The hard label comes out of four measurable things about #124: one of its regions is locked to one row or column, its smallest color spans 3 squares, its least crowded row meets 2 colors, and its largest and smallest regions differ by 17. Boards that score tight on those measures give up their first queen fast.
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.
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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #124 is row 5.
As a sanity check rather than a spoiler: the finished solution to #124 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
- The board is an N×N grid divided into N colored regions.
- Place exactly one queen (♛) in each row, each column, and each colored region.
- No two queens may touch each other — not horizontally, vertically, or diagonally.
- 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.
- 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 #124?
Puzzle #124 is rated hard. 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 #124 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #124, 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 #124?
Start with the indigo region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.