8x8 Queens Puzzle #298
Difficulty: medium. 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 11-step reasoning is written out below.
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Step-by-step solution for puzzle #298
What follows is a complete solve of puzzle #298, worked the way a person works it rather than the way a computer does. It runs to 11 deductions — 8 queen placements and 3 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: last square in a region, region confined to one line, region shadow.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 8, column 8 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 8, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (3 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 3. Only row 2, column 1 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 1, in amber and in the ring around that square is now dead.
Step 4. The mint region is down to one open square, at row 4, column 2. Every colour holds exactly one queen, so that square is forced. Row 4 and column 2 are now spoken for, along with the squares touching that queen.
The board after step 4 — 3 of 8 queens placed. Step 5. Blue is down to 2 candidates in rows 3 and 6, columns 3 and 4, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 6. The pale yellow region is down to one open square, at row 7, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 3, the remaining pale yellow squares, and the ring of neighbours around row 7, column 3.
Step 7. Only row 3, column 4 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 4, in blue and in the ring around that square is now dead.
The board after step 7 — 5 of 8 queens placed. Step 8. Slate is down to 4 candidates in rows 5 and 6, columns 5–7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
Step 9. Only row 6, column 5 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 5, the rest of the red region and every square adjacent to it — diagonals included.
Step 10. The slate region is down to one open square, at row 5, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 7, the remaining slate squares, and the ring of neighbours around row 5, column 7.
Step 11. Only row 1, column 6 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 6, in indigo and in the ring around that square is now dead.
The board after step 11 — 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 #298
Board #298 of the 8x8 bank carries a medium 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, #298 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 #298 are: khaki (1 square), indigo (5 squares), amber (5 squares), mint (5 squares), red (8 squares), pale yellow (10 squares), blue (14 squares), slate (16 squares). An even split would hand every color 8 squares, so the khaki region is running 7 squares under that average while the slate region is the roomiest area on the grid with 16 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So khaki, with 1 square, is under far more pressure than slate with 16. A 15-square gap like this one rewards players who start where the choices are fewest.
A region's outline can constrain it more than its size does. Here khaki is the most solid, filling 100% of its 1×1 box, and blue the most diffuse at 47% of its 5×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Here is the full footprint of every color on puzzle #298, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Khaki covers 1 square, spanning 1 row and 1 column (rows 8–8, columns 8–8). It never leaves row 8, so its queen is locked to that row.
Indigo occupies 5 squares within rows 1–2, columns 5–8.
Amber: 5 squares across rows 1–2, columns 1–4.
Mint covers 5 squares, spanning 3 rows and 2 columns (rows 2–4, columns 1–2).
Red occupies 8 squares within rows 6–8, columns 5–8.
Pale yellow: 10 squares across rows 6–8, columns 1–5.
Blue covers 14 squares, spanning 5 rows and 6 columns (rows 2–6, columns 1–6).
Slate occupies 16 squares within rows 2–6, columns 4–8.
Where to start on this board
Khaki is the natural opening on #298: it is the smallest region on the grid at 1 square, boxed into rows 8–8 and columns 8–8. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because khaki never leaves row 8, its queen must be in that row — and that instantly settles row 8 for everyone else. Sweep along it and X out every square that is not khaki. 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. Amber 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 #298
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 5 and 7 are the narrowest, touched by only 2 colors. Columns 3 and 7 are the tightest columns, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 7 rows. Row 2 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
The middle of #298 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
The whole middle game reduces to two sweeps. Sweep the eight colors looking for one with a single square left; sweep the eight rows and eight columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 8x8 solve from a stalled one.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #298 is rated medium
The rating reflects how much the board concedes up front. Puzzle #298 has two regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 15 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #298, start hunting for it near row 1.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 5 queens in the middle, including 1 in a corner. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #298?
Puzzle #298 is rated medium. Its smallest color region holds 1 square, 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 8x8 puzzle #298 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #298, 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 #298?
Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.