9x9 Queens Puzzle #124
Difficulty: hard. Place 9 queens on this 9x9 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 17-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 17 deductions — 9 queen placements and 8 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 rows, pairing argument on columns, last square in a row, region confined to one line, last square in a region.
Show the full walkthrough (10 steps) — contains the solution
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.
Step 2. Blue is down to 4 candidates in rows 1–3, columns 8 and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 3. Indigo, amber, and blue are now boxed into rows 1–3 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 12 squares at once.
The board after step 3 — 0 of 9 queens placed. Step 4. Wherever slate 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 5. Blue and pale yellow are now boxed into columns 8 and 9 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 4 squares at once.
Step 6. Row 3 has a single open square left, at column 9 in the blue region. Every row needs a queen, so this one is forced. Row 3 and column 9 are now spoken for, along with the squares touching that queen.
Step 7. Pale yellow cannot leave column 8 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 1 square in all.
The board after step 7 — 1 of 9 queens placed. Step 8. Orange is down to 4 candidates in rows 7–9, columns 6 and 7, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about orange itself.
Step 9. Amber and orange are now boxed into columns 6 and 7 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 5 squares at once.
Step 10. 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: 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 2; pale yellow has one square left, so its queen takes row 7, column 8; row 6 is down to one square, putting a queen on row 6, column 4; indigo has one square left, so its queen takes row 1, column 3; khaki has one square left, so its queen takes row 8, column 1; orange has one square left, so its queen takes row 9, column 7; amber has one square left, so its queen takes row 2, column 6. 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 6.
The board after step 10 — 9 of 9 queens placed.
That completes the board: 9 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 9x9 Queens puzzle #124
This is puzzle number 124 in the 9x9 collection, rated hard. The grid holds 81 squares split between nine colored regions, and a finished board carries nine 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 (4 squares), amber (6 squares), orange (6 squares), khaki (8 squares), pale yellow (9 squares), slate (12 squares), mint (15 squares), red (18 squares). An even split would hand every color 9 squares, so the indigo region is running 6 squares under that average while the red region is the roomiest area on the grid with 18 squares.
Every color takes one queen and one only, whatever its size — which is why the 15 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.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #124, packing 75% of its 2×2 bounding box, whereas mint straggles across its 7×5 box at just 43%. 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 #124, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo covers 3 squares, spanning 2 rows and 2 columns (rows 1–2, columns 3–4).
Blue occupies 4 squares within rows 1–3, columns 8–9.
Amber: 6 squares across rows 1–3, columns 6–8.
Orange covers 6 squares, spanning 3 rows and 3 columns (rows 7–9, columns 6–8).
Khaki occupies 8 squares within rows 4–8, columns 1–3.
Pale yellow: 9 squares across rows 4–9, columns 8–9.
Slate covers 12 squares, spanning 5 rows and 4 columns (rows 1–5, columns 1–4).
Mint occupies 15 squares within rows 1–7, columns 4–8.
Red: 18 squares across rows 5–9, columns 1–6.
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 3 to column 4. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: indigo, blue and pale yellow span only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.
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, row 9 is the narrowest, touched by only 3 colors. Columns 5 and 9 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 8 rows. Row 7 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.
The whole middle game reduces to two sweeps. Sweep the nine colors looking for one with a single square left; sweep the nine rows and nine columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 9x9 solve from a stalled one.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #124 is rated hard
The rating reflects how much the board concedes up front. Puzzle #124 has no region confined to a single row or column, its smallest color holds 3 squares, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 15 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.
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 9x9
At 9x9 a full re-scan after every move starts to get slow, so work locally instead. Once a queen goes down, check only the regions, rows and columns that placement actually touched — that is where new information appeared. Fall back to a complete sweep only when the local pass turns up nothing, and your solve times will drop noticeably.
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 column 5.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 5 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
- 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 9x9 Queens puzzle #124?
Puzzle #124 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 9x9 puzzle #124 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #124, has been verified to have exactly one valid arrangement of nine 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 3–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.