9x9 Queens Puzzle #154
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #154
What follows is a complete solve of puzzle #154, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 9 queen placements and 9 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, last square in a region, line confined to one region, pairing argument on rows.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Wherever indigo ends up among its 6 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 (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 8 squares come off.
Step 3. Only row 7, column 2 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 2, in pale yellow and in the ring around that square is now dead.
Step 4. All of the indigo region's remaining squares (4 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
The board after step 4 — 1 of 9 queens placed. Step 5. Amber is down to 4 candidates in rows 2 and 3, columns 7–9, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 6. All of the orange region's remaining squares (3 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 7. Wherever red 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 8. Every open square left in row 8 (5 open squares) belongs to the khaki region. Since that row must contain a queen, khaki is the colour that supplies it — so khaki squares anywhere else on the board are out, 11 squares in all.
The board after step 8 — 1 of 9 queens placed. Step 9. Amber and blue are now boxed into rows 2 and 3 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 7 squares at once.
Step 10. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: 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 4; slate has one square left, so its queen takes row 5, column 6; indigo has one square left, so its queen takes row 1, column 5. 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 1, column 5.
Step 11. All of the khaki region's remaining squares (2 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 12. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: orange has one square left, so its queen takes row 9, column 7; khaki has one square left, so its queen takes row 8, column 9; amber has one square left, so its queen takes row 2, column 8; blue has one square left, so its queen takes row 3, 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 3, column 1.
The board after step 12 — 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 #154
Board #154 of the 9x9 bank carries a hard rating. Its 81 squares are shared between nine colored regions, and the solution places nine queens: one per row, one per column, one per region, none of them side by side or corner to corner.
Puzzle #154 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #154 are: blue (3 squares), orange (3 squares), pale yellow (4 squares), slate (5 squares), indigo (6 squares), amber (7 squares), mint (13 squares), red (14 squares), khaki (26 squares). An even split would hand every color 9 squares, so the blue region is running 6 squares under that average while the khaki region is the roomiest area on the grid with 26 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Blue has only 3 places to put its queen; khaki has 26. The spread between them on this board is 23 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
A region's outline can constrain it more than its size does. Here blue is the most solid, filling 100% of its 3×1 box, and indigo the most diffuse at 60% of its 2×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Blue covers 3 squares, spanning 3 rows and 1 column (rows 1–3, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Orange occupies 3 squares within rows 9–9, columns 6–8. It never leaves row 9, so its queen is locked to that row.
Pale yellow: 4 squares across rows 5–7, columns 1–2.
Slate covers 5 squares, spanning 3 rows and 2 columns (rows 4–6, columns 5–6).
Indigo occupies 6 squares within rows 1–2, columns 2–6.
Amber: 7 squares across rows 1–3, columns 7–9.
Mint covers 13 squares, spanning 3 rows and 6 columns (rows 2–4, columns 1–6).
Red occupies 14 squares within rows 5–9, columns 1–4.
Khaki: 26 squares across rows 3–9, columns 4–9.
Where to start on this board
Open on the tightest color. Here that is blue, confined to 3 squares between rows 1 and 3 and columns 1 and 1. Its queen has nowhere else to go, which means those 3 rows and 1 column carry more constraint than anywhere else on #154.
Because blue stays inside column 1, its queen belongs to that column and no other region may use it. Cross out the rest of column 1 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. Orange and indigo 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 #154
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. Column 9 is the tightest column, 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 8 rows. By contrast row 6 meets 4 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
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.
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 #154 is rated hard
Ratings track how generous the opening is. On #154 you get two regions pinned to a single row or column, a smallest color of 3 squares, a tightest row crossed by 2 colors, and a 23-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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.
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 #154 the place to look for one is around row 8.
As a sanity check rather than a spoiler: the finished solution to #154 puts 4 queens on the outer border and 5 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 9x9 Queens puzzle #154?
Puzzle #154 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #154 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #154, 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 #154?
Start with the blue region — the most constrained color on this board, with 3 squares spanning rows 1–3 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.