8x8 Queens Puzzle #242
Difficulty: hard. 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 16-step reasoning is written out below.
Previous puzzle · All 8x8 puzzles · Next puzzle
Step-by-step solution for puzzle #242
What follows is a complete solve of puzzle #242, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 8 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 region shadow.
Techniques this board needs: region shadow, region confined to one line, last square in a region.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Wherever indigo 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 2. All of the mint region's remaining squares (2 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 8 squares come off.
Step 3. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 6 squares in all.
The board after step 3 — 0 of 8 queens placed. Step 4. Wherever amber 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 5. Blue cannot leave column 4 — every one of its open squares (3 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 6 squares in all.
Step 6. The pale yellow region has 4 squares left, spread across rows 6–8, columns 6 and 7. 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 7. Khaki cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 9 squares in all.
The board after step 7 — 0 of 8 queens placed. Step 8. The amber region is down to one open square, at row 2, column 1. Every colour holds exactly one queen, so that square is forced. Row 2 and column 1 are now spoken for, along with the squares touching that queen.
Step 9. Blue cannot leave column 4 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 2 squares in all.
Step 10. 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: red has one square left, so its queen takes row 6, column 3; khaki has one square left, so its queen takes row 8, column 2; pale yellow has one square left, so its queen takes row 7, column 7; indigo has one square left, so its queen takes row 1, column 6; 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 8. 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 4, column 8.
The board after step 10 — 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 #242
Board #242 of the 8x8 bank carries a hard 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.
Like every board on this site, #242 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 #242 are: mint (2 squares), khaki (2 squares), indigo (4 squares), amber (5 squares), blue (6 squares), pale yellow (7 squares), red (13 squares), slate (25 squares). An even split would hand every color 8 squares, so the mint region is running 6 squares under that average while the slate region is the roomiest area on the grid with 25 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Mint is working with 2 squares while slate has 25 to spare, a gap of 23. Attack the cramped end and the roomy regions tend to resolve themselves.
Look at arrangement as well as area. Mint is the densest region on this grid at 100% of a 2×1 frame; slate is the loosest, occupying only 52% of its 8×6 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 hard board.
Mint occupies 2 squares within rows 3–4, columns 8–8. It sits wholly inside column 8, so its queen must be in that column.
Khaki: 2 squares across rows 7–8, columns 2–2. It sits wholly inside column 2, so its queen must be in that column.
Indigo covers 4 squares, spanning 2 rows and 3 columns (rows 1–2, columns 6–8).
Amber occupies 5 squares within rows 1–3, columns 1–2.
Blue: 6 squares across rows 1–4, columns 3–4.
Pale yellow covers 7 squares, spanning 3 rows and 3 columns (rows 6–8, columns 6–8).
Red occupies 13 squares within rows 3–8, columns 1–3.
Slate: 25 squares across rows 1–8, columns 3–8.
Where to start on this board
Mint is the natural opening on #242: it is the smallest region on the grid at 2 squares, boxed into rows 3–4 and columns 8–8. Since one of those squares must hold a queen, that block of 2 rows and 1 column is the most contested part of the board.
Because mint stays inside column 8, its queen belongs to that column and no other region may use it. Cross out the rest of column 8 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. Indigo 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 #242
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. Column 5 is the tightest column, with 1 color.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 7 rows. Row 3 is the crowded extreme at 5 colors — worth revisiting later, not now.
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.
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.
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 #242 is rated hard
The hard label comes out of four measurable things about #242: two of its regions are 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 23. Boards that score tight on those measures give up their first queen fast.
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 #242 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 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.
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 column 5 on this board.
A non-spoiling distribution check: solved, #242 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 8x8 Queens puzzle #242?
Puzzle #242 is rated hard. 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 8x8 puzzle #242 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #242, 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 #242?
Start with the mint region — the most constrained color on this board, with 2 squares spanning rows 3–4 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.