9x9 Queens Puzzle #294
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 14-step reasoning is written out below.
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Step-by-step solution for puzzle #294
What follows is a complete solve of puzzle #294, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 9 queen placements and 5 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 region shadow.
Techniques this board needs: region shadow, region confined to one line, last square in a region.
Show the full walkthrough (8 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. Amber is down to 3 candidates in rows 1 and 2, columns 1 and 2, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. Red cannot leave column 9 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 9 squares in all.
Step 4. All of the pale yellow region's remaining squares (2 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 10 squares come off.
The board after step 4 — 0 of 9 queens placed. Step 5. Only row 1, column 6 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 6, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 6. The amber region is down to one open square, at row 2, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 2, the remaining amber squares, and the ring of neighbours around row 2, column 2.
Step 7. Slate cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 7 squares in all.
Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: 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 7; red has one square left, so its queen takes row 6, column 9; slate has one square left, so its queen takes row 5, column 5; blue has one square left, so its queen takes row 3, column 4; mint has one square left, so its queen takes row 4, column 1; khaki has one square left, so its queen takes row 8, column 3. 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 3.
The board after step 8 — 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 #294
Board #294 of the 9x9 bank carries a easy 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.
Like every board on this site, #294 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 #294 are: red (2 squares), pale yellow (2 squares), indigo (3 squares), amber (3 squares), slate (5 squares), mint (11 squares), orange (11 squares), khaki (14 squares), blue (30 squares). An even split would hand every color 9 squares, so the red region is running 7 squares under that average while the blue region is the roomiest area on the grid with 30 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Red has only 2 places to put its queen; blue has 30. The spread between them on this board is 28 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 red is the most solid, filling 100% of its 2×1 box, and blue the most diffuse at 71% of its 6×7 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.
Red: 2 squares across rows 6–7, columns 9–9. It sits wholly inside column 9, so its queen must be in that column.
Pale yellow covers 2 squares, spanning 2 rows and 1 column (rows 7–8, columns 7–7). It sits wholly inside column 7, so its queen must be in that column.
Indigo occupies 3 squares within rows 1–2, columns 6–7.
Amber: 3 squares across rows 1–2, columns 1–2.
Slate covers 5 squares, spanning 3 rows and 2 columns (rows 5–7, columns 5–6).
Mint occupies 11 squares within rows 2–6, columns 1–3.
Orange: 11 squares across rows 7–9, columns 5–9.
Khaki covers 14 squares, spanning 4 rows and 4 columns (rows 6–9, columns 1–4).
Blue occupies 30 squares within rows 1–6, columns 3–9.
Where to start on this board
Open on the tightest color. Here that is red, confined to 2 squares between rows 6 and 7 and columns 9 and 9. Its queen has nowhere else to go, which means those 2 rows and 1 column carry more constraint than anywhere else on #294.
Because red stays inside column 9, its queen belongs to that column and no other region may use it. Cross out the rest of column 9 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, indigo and pale yellow 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 #294
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3, 4 and 9 are the narrowest, touched by only 2 colors. Columns 4 and 8 are the tightest columns, 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 7 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
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
With nine queens to seat and nine regions competing over 81 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 9x9 boards quickly and players who stall halfway.
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 #294 is rated easy
Ratings track how generous the opening is. On #294 you get two regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 28-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
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.
If #294 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.
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 #294 the place to look for one is around row 3.
As a sanity check rather than a spoiler: the finished solution to #294 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 #294?
Puzzle #294 is rated easy. Its smallest color region holds 2 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 #294 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #294, 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 #294?
Start with the red region — the most constrained color on this board, with 2 squares spanning rows 6–7 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.