8x8 Queens Puzzle #294
Difficulty: easy. Place 8 queens on this 8x8 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 #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 18 deductions — 8 queen placements and 10 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 shadow, pairing argument on rows, region confined to one line, pairing argument on columns, last square in a region.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Wherever indigo ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. Mint is down to 3 candidates in rows 4 and 5, columns 7 and 8, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about mint itself.
Step 3. Slate, red, pale yellow, and khaki are now boxed into rows 5–8 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 5 squares at once.
Step 4. All of the mint region's remaining squares (2 open squares) lie in row 4. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 7 squares come off.
Step 5. Blue is down to 4 candidates in rows 1–3, columns 1 and 3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
The board after step 5 — 0 of 8 queens placed. Step 6. Here is the pairing argument. The indigo and mint regions have no open squares outside columns 7 and 8 — 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: 6 squares come off in one stroke.
Step 7. Slate cannot leave column 6 — 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: 6 squares in all.
Step 8. The khaki region is down to one open square, at row 8, column 5. Every colour holds exactly one queen, so that square is forced. Row 8 and column 5 are now spoken for, along with the squares touching that queen.
Step 9. Red cannot leave row 6 — every one of its open squares (3 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 3 squares in all.
Step 10. The slate region is down to one open square, at row 5, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 6, the remaining slate squares, and the ring of neighbours around row 5, column 6.
The board after step 10 — 2 of 8 queens placed. Step 11. Only row 4, column 8 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 8, in mint and in the ring around that square is now dead.
Step 12. The indigo region is down to one open square, at row 1, column 7. Every colour holds exactly one queen, so that square is forced. Row 1 and column 7 are now spoken for, along with the squares touching that queen.
Step 13. Wherever amber ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 14. 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: 2 squares come off.
Step 15. 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: pale yellow has one square left, so its queen takes row 7, column 2; red has one square left, so its queen takes row 6, column 4; amber has one square left, so its queen takes row 2, column 3; 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 15 — 8 of 8 queens placed.
That completes the board: 8 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 8x8 Queens puzzle #294
Board #294 of the 8x8 bank carries a easy rating. Its 64 squares are shared between eight colored regions, and the solution places eight queens: one per row, one per column, one per region, none of them side by side or corner to corner.
As with every puzzle in this collection, #294 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #294 are: mint (3 squares), indigo (5 squares), khaki (5 squares), red (6 squares), slate (7 squares), blue (8 squares), pale yellow (9 squares), amber (21 squares). An even split would hand every color 8 squares, so the mint region is running 5 squares under that average while the amber region is the roomiest area on the grid with 21 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Mint has only 3 places to put its queen; amber has 21. The spread between them on this board is 18 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Look at arrangement as well as area. Indigo is the densest region on this grid at 83% of a 3×2 frame; blue is the loosest, occupying only 53% of its 5×3 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Below is every color on #294 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Mint: 3 squares across rows 4–5, columns 7–8.
Indigo covers 5 squares, spanning 3 rows and 2 columns (rows 1–3, columns 7–8).
Khaki occupies 5 squares within rows 7–8, columns 5–7.
Red: 6 squares across rows 6–7, columns 2–5.
Slate covers 7 squares, spanning 4 rows and 3 columns (rows 5–8, columns 6–8).
Blue occupies 8 squares within rows 1–5, columns 1–3.
Pale yellow: 9 squares across rows 5–8, columns 1–4.
Amber covers 21 squares, spanning 5 rows and 6 columns (rows 1–5, columns 2–7).
Where to start on this board
Mint is the natural opening on #294: it is the smallest region on the grid at 3 squares, boxed into rows 4–5 and columns 7–8. Since one of those squares must hold a queen, that block of 2 rows and 2 columns is the most contested part of the board.
With 2 rows and 2 columns of room, mint needs narrowing rather than solving outright. Test its 3 squares against the neighbours: a candidate that would strand another color is dead, and eliminating even two of them tightens the whole corner of the board around rows 4–5.
Work outward to the other flat regions next. Red 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 #294
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3, 4, 6 and 8 are the narrowest, touched by only 3 colors. Column 1 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 7 rows. Row 5 is the crowded extreme at 5 colors — worth revisiting later, not now.
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 eight queens to seat and eight regions competing over 64 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 8x8 boards quickly and players who stall halfway.
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 #294 is rated easy
What earns a board its rating is the shape of its opening. Here that opening offers no single-line region at all, a 3-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 18. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
Techniques that work well at 8x8
At 8x8 the whole grid stays within a single glance, which makes systematic scanning practical. Read the rows in order and count the colors in each — a row touched by two colors is far more constrained than one touched by five, and that is usually where the next forced move hides. The board is small enough that re-scanning from the top after each placement costs almost nothing.
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 column 1.
A non-spoiling distribution check: solved, #294 carries 4 queens on the perimeter against 4 queens inside, with the corners empty. 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 8x8 Queens puzzle #294?
Puzzle #294 is rated easy. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 8x8 puzzle #294 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #294, has been verified to have exactly one valid arrangement of eight 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 mint region — the most constrained color on this board, with 3 squares spanning rows 4–5 and columns 7–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.