9x9 Queens Puzzle #160
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #160
What follows is a complete solve of puzzle #160, 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 columns.
Techniques this board needs: region confined to one line, region shadow, pairing argument on rows, pairing argument on columns, last square in a region.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (4 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 5 squares in all.
Step 2. Amber is down to 3 candidates in rows 2 and 3, columns 1 and 2, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 1 square in all.
The board after step 3 — 0 of 9 queens placed. Step 4. 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: 7 squares come off.
Step 5. Red, pale yellow, and khaki are now boxed into rows 6–8 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 4 squares at once.
Step 6. Here is the pairing argument. The amber and red regions have no open squares outside columns 1 and 2 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 4 squares come off in one stroke.
Step 7. Mint cannot leave column 3 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 8 squares in all.
The board after step 7 — 0 of 9 queens placed. Step 8. 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: 1 square come off.
Step 9. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 4 squares in all.
Step 10. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 5; indigo has one square left, so its queen takes row 1, column 4; mint has one square left, so its queen takes row 4, column 3; khaki has one square left, so its queen takes row 8, column 6; orange has one square left, so its queen takes row 9, column 8; pale yellow has one square left, so its queen takes row 7, column 9; slate has one square left, so its queen takes row 5, column 7; red has one square left, so its queen takes row 6, column 2; amber has one square left, so its queen takes row 2, 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 2, column 1.
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 #160
This is puzzle number 160 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.
Like every board on this site, #160 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #160 are: orange (3 squares), indigo (4 squares), amber (4 squares), red (7 squares), mint (8 squares), pale yellow (8 squares), blue (13 squares), khaki (14 squares), slate (20 squares). An even split would hand every color 9 squares, so the orange region is running 6 squares under that average while the slate region is the roomiest area on the grid with 20 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Orange is working with 3 squares while slate has 20 to spare, a gap of 17. Attack the cramped end and the roomy regions tend to resolve themselves.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #160, packing 100% of its 1×4 bounding box, whereas pale yellow straggles across its 4×4 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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.
Orange covers 3 squares, spanning 1 row and 3 columns (rows 9–9, columns 6–8). It never leaves row 9, so its queen is locked to that row.
Indigo occupies 4 squares within rows 1–1, columns 2–5. It never leaves row 1, so its queen is locked to that row.
Amber: 4 squares across rows 1–3, columns 1–2.
Red covers 7 squares, spanning 4 rows and 2 columns (rows 6–9, columns 1–2).
Mint occupies 8 squares within rows 2–6, columns 1–3.
Pale yellow: 8 squares across rows 6–9, columns 6–9.
Blue covers 13 squares, spanning 4 rows and 6 columns (rows 1–4, columns 4–9).
Khaki occupies 14 squares within rows 6–9, columns 3–7.
Slate: 20 squares across rows 3–6, columns 2–9.
Where to start on this board
Begin where the choices are fewest. On this board that means orange, which owns just 3 squares inside a 1×3 window running from row 9 to row 9 and column 6 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 orange never leaves row 9, its queen must be in that row — and that instantly settles row 9 for everyone else. Sweep along it and X out every square that is not orange. Then look at which colors just lost ground: on a grid this size that one observation usually forces a second region within a move or two.
Work outward to the other flat regions next. Indigo 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 #160
A quick way to find the next move is to count how many different colors touch each line. On this board, row 5 is the narrowest, touched by only 2 colors. Columns 1 and 9 are the tightest columns, with 3 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 5 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.
Resist the plausible-looking queen. On #160 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 #160 is rated easy
Ratings track how generous the opening is. On #160 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 17-square gap between the largest and smallest regions. Those four numbers largely explain the easy 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.
If #160 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 5 on this board.
As a sanity check rather than a spoiler: the finished solution to #160 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 #160?
Puzzle #160 is rated easy. 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 #160 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #160, 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 #160?
Start with the orange region — the most constrained color on this board, with 3 squares spanning rows 9–9 and columns 6–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.