9x9 Queens Puzzle #184
Difficulty: easy. 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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #184
What follows is a complete solve of puzzle #184, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 9 queen placements and 6 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 confined to one line, region shadow, pairing argument on rows, last square in a region.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Indigo cannot leave column 3 — every one of its open squares (2 open squares) sits there. That column belongs to indigo, so every square in it owned by another colour is dead: 11 squares in all.
Step 2. Khaki is down to 3 candidates in rows 8 and 9, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about khaki itself.
Step 3. The orange region has 3 squares left, spread across rows 8 and 9, columns 8 and 9. 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.
The board after step 3 — 0 of 9 queens placed. Step 4. Here is the pairing argument. The khaki and orange regions have no open squares outside rows 8 and 9 — 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: 8 squares come off in one stroke.
Step 5. Only row 7, column 8 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 8, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 6. The orange region is down to one open square, at row 9, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 9, the remaining orange squares, and the ring of neighbours around row 9, column 9.
Step 7. Only row 8, column 1 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 1, in khaki and in the ring around that square is now dead.
The board after step 7 — 3 of 9 queens placed. Step 8. All of the blue region's remaining squares (2 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
Step 9. The mint region has 3 squares left, spread across rows 4 and 5, columns 4 and 5. 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 10. 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: red has one square left, so its queen takes row 6, column 5; mint has one square left, so its queen takes row 4, column 4; blue has one square left, so its queen takes row 3, column 2; indigo has one square left, so its queen takes row 1, column 3; amber has one square left, so its queen takes row 2, column 6; slate has one square left, so its queen takes row 5, column 7. 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 5, column 7.
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 #184
This is puzzle number 184 in the 9x9 collection, rated easy. 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.
There is exactly one way to finish #184, 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 nine regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #184 are: indigo (2 squares), orange (3 squares), khaki (4 squares), pale yellow (6 squares), red (8 squares), blue (10 squares), amber (11 squares), mint (14 squares), slate (23 squares). An even split would hand every color 9 squares, so the indigo region is running 7 squares under that average while the slate region is the roomiest area on the grid with 23 squares.
Every color takes one queen and one only, whatever its size — which is why the 21 square difference between indigo and slate 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.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 2×1 frame; amber is the loosest, occupying only 55% of its 4×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Here is the full footprint of every color on puzzle #184, 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 2 squares, spanning 2 rows and 1 column (rows 1–2, columns 3–3). It sits wholly inside column 3, so its queen must be in that column.
Orange occupies 3 squares within rows 8–9, columns 8–9.
Khaki: 4 squares across rows 8–9, columns 1–3.
Pale yellow covers 6 squares, spanning 3 rows and 3 columns (rows 7–9, columns 6–8).
Red occupies 8 squares within rows 6–9, columns 4–5.
Blue: 10 squares across rows 1–5, columns 1–3.
Amber covers 11 squares, spanning 4 rows and 5 columns (rows 1–4, columns 4–8).
Mint occupies 14 squares within rows 4–8, columns 1–5.
Slate: 23 squares across rows 1–7, columns 6–9.
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 2 squares inside a 2×1 window running from row 1 to row 2 and column 3 to column 3. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because indigo stays inside column 3, its queen belongs to that column and no other region may use it. Cross out the rest of column 3 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.
Work outward to the other flat regions next. Khaki and orange are no more than two rows tall, so their queens are 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 #184
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3, 5 and 6 are the narrowest, touched by only 3 colors. Column 9 is the tightest column, with 2 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 8 rows. Row 8 is the crowded extreme at 5 colors — worth revisiting later, not now.
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 81 squares of this grid. First: has any of the nine regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 9x9 boards almost always run one of those checks and forget the other.
Resist the plausible-looking queen. On #184 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 #184 is rated easy
The rating reflects how much the board concedes up front. Puzzle #184 has one region confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 21 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 #184 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 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 #184 is column 9.
A non-spoiling distribution check: solved, #184 carries 3 queens on the perimeter against 6 queens inside, 1 of them cornered. 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
- 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 #184?
Puzzle #184 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #184 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #184, 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 #184?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–2 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.