9x9 Queens Puzzle #140
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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #140
What follows is a complete solve of puzzle #140, 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 rows.
Techniques this board needs: region confined to one line, region shadow, pairing argument on rows, last square in a region, last square in a row.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Indigo cannot leave column 1 — 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: 9 squares in all.
Step 2. Orange is down to 3 candidates in rows 8 and 9, columns 4 and 5, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about orange itself.
Step 3. The pale yellow region has 4 squares left, spread across rows 7–9, columns 2 and 3. 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 4. Here is the pairing argument. The indigo and amber regions have no open squares outside rows 1 and 2 — 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: 9 squares come off in one stroke.
The board after step 4 — 0 of 9 queens placed. Step 5. Blue is down to 3 candidates in rows 3 and 4, columns 2 and 3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 6. Here is the pairing argument. The blue and mint regions have no open squares outside rows 3 and 4 — 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: 6 squares come off in one stroke.
Step 7. Khaki and orange are now boxed into rows 8 and 9 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 6 squares at once.
Step 8. 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 3; 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 1; amber has one square left, so its queen takes row 2, column 8; mint has one square left, so its queen takes row 4, column 9; row 8 is down to one square, putting a queen on row 8, 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 8, column 7.
The board after step 8 — 6 of 9 queens placed. Step 9. All of the slate region's remaining squares (3 open squares) lie in row 5. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 10. Only row 6, column 6 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 6, in red and in the ring around that square is now dead.
Step 11. The slate region is down to one open square, at row 5, column 4. Every colour holds exactly one queen, so that square is forced. Row 5 and column 4 are now spoken for, along with the squares touching that queen.
Step 12. Only row 9, column 5 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 5, the rest of the orange region and every square adjacent to it — diagonals included.
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 #140
This is puzzle number 140 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 #140, 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 #140 are: indigo (2 squares), orange (3 squares), amber (5 squares), khaki (5 squares), mint (8 squares), pale yellow (8 squares), blue (14 squares), red (16 squares), slate (20 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 20 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Indigo is working with 2 squares while slate has 20 to spare, a gap of 18. Attack the cramped end and the roomy regions tend to resolve themselves.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 2×1 frame; blue is the loosest, occupying only 56% of its 5×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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 easy board.
Indigo occupies 2 squares within rows 1–2, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Orange: 3 squares across rows 8–9, columns 4–5.
Amber covers 5 squares, spanning 2 rows and 4 columns (rows 1–2, columns 6–9).
Khaki occupies 5 squares within rows 8–9, columns 6–8.
Mint: 8 squares across rows 2–4, columns 6–9.
Pale yellow covers 8 squares, spanning 3 rows and 3 columns (rows 7–9, columns 1–3).
Blue occupies 14 squares within rows 1–5, columns 1–5.
Red: 16 squares across rows 5–9, columns 5–9.
Slate covers 20 squares, spanning 5 rows and 7 columns (rows 3–7, columns 1–7).
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 1 to column 1. 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 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. Amber, orange and khaki 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 #140
A quick way to find the next move is to count how many different colors touch each line. On this board, row 6 is the narrowest, touched by only 2 colors. Columns 2, 3, 4 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 9 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.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #140 is rated easy
The easy label comes out of four measurable things about #140: one of its regions is locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 2 colors, and its largest and smallest regions differ by 18. Boards that score tight on those measures give up their first queen fast.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a easy board from the rest.
Stuck on #140 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.
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 6 on this board.
As a sanity check rather than a spoiler: the finished solution to #140 puts 3 queens on the outer border and 6 queens in the interior, 1 of them in an actual 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 #140?
Puzzle #140 is rated easy. Its smallest color region holds 2 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 9x9 puzzle #140 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #140, 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 #140?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–2 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.