7x7 Queens Puzzle #183
Difficulty: hard. 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 18-step reasoning is written out below.
Previous puzzle · All 7x7 puzzles · Next puzzle
Step-by-step solution for puzzle #183
What follows is a complete solve of puzzle #183, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 7 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 proof by contradiction.
Techniques this board needs: region shadow, region confined to one line, pairing argument on rows, pairing argument on columns, proof by contradiction, last square in a region.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Wherever blue ends up among its 3 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
Step 2. Mint is down to 4 candidates in rows 3–5, columns 6 and 7, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about mint itself.
Step 3. Red cannot leave column 1 — every one of its open squares (4 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 3 squares in all.
Step 4. All of the indigo 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: 5 squares come off.
The board after step 4 — 0 of 7 queens placed. Step 5. Blue is down to 2 candidates in rows 2 and 3, columns 3 and 4, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 6. Here is the pairing argument. The indigo, amber, and blue regions have no open squares outside rows 1–3 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 3 squares come off in one stroke.
Step 7. Mint cannot leave column 6 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 6 squares in all.
Step 8. Slate is down to 2 candidates in rows 4 and 5, columns 3 and 4, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about slate itself.
The board after step 8 — 0 of 7 queens placed. Step 9. Mint and slate are now boxed into rows 4 and 5 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 2 squares at once.
Step 10. Here is the pairing argument. The blue and slate regions have no open squares outside columns 3 and 4 — 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: 4 squares come off in one stroke.
Step 11. Test row 3, column 2 for indigo: place a queen there, run the forced consequences through, and column 3 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 12. 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: indigo has one square left, so its queen takes row 1, column 2; amber has one square left, so its queen takes row 2, column 7; blue has one square left, so its queen takes row 3, column 3; slate has one square left, so its queen takes row 5, column 4; 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 5; red has one square left, so its queen takes row 6, 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 6, column 1.
The board after step 12 — 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 #183
7x7 puzzle #183 is rated hard. Seven colored regions cover its 49 squares, and your job is to seat seven queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
As with every puzzle in this collection, #183 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 #183 are: blue (3 squares), mint (4 squares), red (4 squares), amber (5 squares), indigo (7 squares), slate (13 squares), pale yellow (13 squares). An even split would hand every color 7 squares, so the blue region is running 4 squares under that average while the pale yellow region is the roomiest area on the grid with 13 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Blue is working with 3 squares while pale yellow has 13 to spare, a gap of 10. Attack the cramped end and the roomy regions tend to resolve themselves.
Look at arrangement as well as area. Red is the densest region on this grid at 100% of a 4×1 frame; slate is the loosest, occupying only 43% of its 6×5 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.
Blue: 3 squares across rows 2–3, columns 3–4.
Mint covers 4 squares, spanning 3 rows and 2 columns (rows 3–5, columns 6–7).
Red occupies 4 squares within rows 4–7, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Amber: 5 squares across rows 1–2, columns 4–7.
Indigo covers 7 squares, spanning 3 rows and 3 columns (rows 1–3, columns 1–3).
Slate occupies 13 squares within rows 2–7, columns 2–6.
Pale yellow: 13 squares across rows 4–7, columns 3–7.
Where to start on this board
The most constrained color is where a solve should begin, and on #183 that is blue with 3 squares. It reaches from row 2 to row 3 and from column 3 to column 4 — 2 rows by 2 columns. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Blue spans 2 rows, so it stays open for now — but it is still the shortest list on the board at 3 squares. Work through those squares first and mark the ones that would leave another region homeless. That pruning is what makes the rest of the grid legible.
Work outward to the other flat regions next. Amber 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 #183
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Columns 1 and 2 are the tightest columns, with 2 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 6 rows. Row 5 sits at the far end with 4 colors crossing it; it will almost certainly be among the last to settle.
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.
Two checks, run alternately, will carry you through the 49 squares of this grid. First: has any of the seven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 7x7 boards almost always run one of those checks and forget the other.
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 #183 is rated hard
The hard label comes out of four measurable things about #183: one of its regions is locked to one row or column, its smallest color spans 3 squares, its least crowded row meets 2 colors, and its largest and smallest regions differ by 10. 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.
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 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.
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 row 1 on this board.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 3 queens in the middle, and nothing in the corners. 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 7x7 Queens puzzle #183?
Puzzle #183 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #183 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #183, 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 #183?
Start with the blue region — the most constrained color on this board, with 3 squares spanning rows 2–3 and columns 3–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.