7x7 Queens Puzzle #18
Difficulty: easy. Place 7 queens on this 7x7 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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #18
What follows is a complete solve of puzzle #18, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 7 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 line confined to one region.
Techniques this board needs: region shadow, region confined to one line, last square in a region, line confined to one region, last square in a row.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Wherever blue ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 2. 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: 8 squares come off.
Step 3. The slate region has 2 squares left, spread across rows 5 and 6, columns 2 and 3. You do not need to know which of them takes the queen: every one of those options attacks the same 4 squares, so they can be crossed out now.
Step 4. The mint region is down to one open square, at row 4, column 1. Every colour holds exactly one queen, so that square is forced. Row 4 and column 1 are now spoken for, along with the squares touching that queen.
Step 5. Amber is down to 2 candidates in rows 2 and 3, columns 2 and 3, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about amber itself.
The board after step 5 — 1 of 7 queens placed. Step 6. The red region has 3 squares left, spread across rows 5 and 6, columns 5 and 6. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 7. Blue cannot leave column 7 — 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: 3 squares in all.
Step 8. Every open square left in row 1 (4 open squares) belongs to the indigo region. Since that row must contain a queen, indigo is the colour that supplies it — so indigo squares anywhere else on the board are out, 5 squares in all.
Step 9. Look along row 2: one square survives, row 2, column 2, which belongs to amber. A row cannot be left empty, so the queen goes there. Everything else in row 2, in column 2, in amber and in the ring around that square is now dead.
Step 10. The slate region is down to one open square, at row 5, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 3, the remaining slate squares, and the ring of neighbours around row 5, column 3.
The board after step 10 — 3 of 7 queens placed. Step 11. Only row 3, column 7 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 7, in blue and in the ring around that square is now dead.
Step 12. All of the red region's remaining squares (2 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 13. Only row 7, column 4 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 4, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 14. The red region is down to one open square, at row 6, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 6, the remaining red squares, and the ring of neighbours around row 6, column 6.
Step 15. Only row 1, column 5 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 5, in indigo and in the ring around that square is now dead.
The board after step 15 — 7 of 7 queens placed.
That completes the board: 7 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 7x7 Queens puzzle #18
Board #18 of the 7x7 bank carries a easy rating. Its 49 squares are shared between seven colored regions, and the solution places seven 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, #18 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 #18 are: mint (2 squares), blue (4 squares), amber (6 squares), slate (6 squares), red (6 squares), pale yellow (11 squares), indigo (14 squares). An even split would hand every color 7 squares, so the mint region is running 5 squares under that average while the indigo region is the roomiest area on the grid with 14 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 mint, with 2 squares, is under far more pressure than indigo with 14. A 12-square gap like this one rewards players who start where the choices are fewest.
Square count is only half the story — how a color is arranged counts too. Mint is the tidiest shape on #18, packing 100% of its 1×2 bounding box, whereas slate straggles across its 3×4 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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 easy board.
Mint: 2 squares across rows 4–4, columns 1–2. It never leaves row 4, so its queen is locked to that row.
Blue covers 4 squares, spanning 3 rows and 2 columns (rows 3–5, columns 6–7).
Amber occupies 6 squares within rows 1–3, columns 1–3.
Slate: 6 squares across rows 4–6, columns 1–4.
Red covers 6 squares, spanning 3 rows and 3 columns (rows 4–6, columns 5–7).
Pale yellow occupies 11 squares within rows 5–7, columns 1–7.
Indigo: 14 squares across rows 1–3, columns 2–7.
Where to start on this board
Begin where the choices are fewest. On this board that means mint, which owns just 2 squares inside a 1×2 window running from row 4 to row 4 and column 1 to column 2. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: blue and mint span only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.
The tightest lines on puzzle #18
A quick way to find the next move is to count how many different colors touch each line. On this board, row 7 is the narrowest, touched by only 1 color. Columns 4 and 5 are the tightest columns, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 1 color, then one of those regions has to own it, and every other region is competing for the remaining 6 rows. By contrast row 5 meets 4 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
Keep alternating between two views of the board. In the region view you ask which of the seven colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 7x7 board unwinds.
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 #18 is rated easy
The easy label comes out of four measurable things about #18: one of its regions is locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 1 color, and its largest and smallest regions differ by 12. Boards that score tight on those measures give up their first queen fast.
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 #18 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 7x7
At 7x7 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 #18, start hunting for it near row 7.
As a sanity check rather than a spoiler: the finished solution to #18 puts 4 queens on the outer border and 3 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 7x7 Queens puzzle #18?
Puzzle #18 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 1 color, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #18 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #18, has been verified to have exactly one valid arrangement of seven queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #18?
Start with the mint region — the most constrained color on this board, with 2 squares spanning rows 4–4 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.