8x8 Queens Puzzle #272
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #272
What follows is a complete solve of puzzle #272, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 8 queen placements and 11 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 confined to one line, region shadow, pairing argument on rows, pairing argument on columns, last square in a region, last square in a column.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (4 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 4 squares in all.
Step 2. All of the red region's remaining squares (2 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 10 squares come off.
Step 3. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 1 square in all.
Step 4. Wherever pale yellow ends up among its 7 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Khaki cannot leave row 8 — every one of its open squares (3 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 4 squares in all.
The board after step 5 — 0 of 8 queens placed. Step 6. The pale yellow region has 4 squares left, spread across rows 6 and 7, columns 1 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 7. Red and pale yellow are now boxed into rows 6 and 7 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 4 squares at once.
Step 8. All of the mint region's remaining squares (2 open squares) lie in column 6. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 9. 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: 1 square in all.
Step 10. Here is the pairing argument. The indigo and blue 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: 1 square come off in one stroke.
The board after step 10 — 0 of 8 queens placed. Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: khaki has one square left, so its queen takes row 8, column 4; red has one square left, so its queen takes row 6, column 5; mint has one square left, so its queen takes row 4, column 6; pale yellow has one square left, so its queen takes row 7, column 1; column 7 is down to one square, putting a queen on row 1, 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 1, column 7.
Step 12. All of the amber region's remaining squares (2 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 13. Only row 5, column 3 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 3, the rest of the slate region and every square adjacent to it — diagonals included.
Step 14. The blue region is down to one open square, at row 3, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 8, the remaining blue squares, and the ring of neighbours around row 3, column 8.
Step 15. Only row 2, column 2 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 2, in amber and in the ring around that square is now dead.
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 #272
This is puzzle number 272 in the 8x8 collection, rated medium. The grid holds 64 squares split between eight colored regions, and a finished board carries eight queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
Like every board on this site, #272 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 #272 are: red (2 squares), indigo (4 squares), amber (6 squares), pale yellow (7 squares), khaki (7 squares), mint (9 squares), blue (10 squares), slate (19 squares). An even split would hand every color 8 squares, so the red region is running 6 squares under that average while the slate region is the roomiest area on the grid with 19 squares.
Every color takes one queen and one only, whatever its size — which is why the 17 square difference between red and slate is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×4 box that encloses it, while mint is the most scattered at 45% of its 5×4 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
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 occupies 2 squares within rows 6–7, columns 5–5. It sits wholly inside column 5, so its queen must be in that column.
Indigo: 4 squares across rows 1–1, columns 5–8. It never leaves row 1, so its queen is locked to that row.
Amber covers 6 squares, spanning 3 rows and 2 columns (rows 1–3, columns 1–2).
Pale yellow occupies 7 squares within rows 6–8, columns 1–3.
Khaki: 7 squares across rows 6–8, columns 4–7.
Mint covers 9 squares, spanning 5 rows and 4 columns (rows 4–8, columns 5–8).
Blue occupies 10 squares within rows 2–5, columns 6–8.
Slate: 19 squares across rows 1–7, columns 1–5.
Where to start on this board
The most constrained color is where a solve should begin, and on #272 that is red with 2 squares. It reaches from row 6 to row 7 and from column 5 to column 5 — 2 rows by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Because red stays inside column 5, its queen belongs to that column and no other region may use it. Cross out the rest of column 5 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 is no more than two rows tall, so its queen is 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 #272
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, 5 and 8 are the narrowest, touched by only 3 colors. Columns 3 and 4 are the tightest columns, 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 7 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.
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 #272 is rated medium
Ratings track how generous the opening is. On #272 you get two regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 3 colors, and a 17-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.
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 #272 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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #272 is column 3.
A non-spoiling distribution check: solved, #272 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 #272?
Puzzle #272 is rated medium. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 8x8 puzzle #272 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #272, 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 #272?
Start with the red region — the most constrained color on this board, with 2 squares spanning rows 6–7 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.