7x7 Queens Puzzle #19
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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #19
What follows is a complete solve of puzzle #19, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 7 queen placements and 10 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 shadow, region confined to one line, pairing argument on rows, pairing argument on columns, last square in a region.
Show the full walkthrough (11 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. Amber is down to 4 candidates in rows 1 and 2, columns 5–7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 3. Mint cannot leave column 3 — 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: 9 squares in all.
Step 4. Wherever slate 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.
The board after step 4 — 0 of 7 queens placed. Step 5. Red is down to 3 candidates in rows 6 and 7, columns 2, 4, and 5, and they overlap enough to cover 4 squares elsewhere. Cross those out without deciding anything about red itself.
Step 6. All of the slate region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 7. 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 5 squares at once.
The board after step 7 — 0 of 7 queens placed. Step 8. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
Step 9. The amber region has 3 squares left, spread across rows 1 and 2, columns 5–7. 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 10. Here is the pairing argument. The blue and pale yellow regions have no open squares outside columns 6 and 7 — 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: 2 squares come off in one stroke.
Step 11. 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: amber has one square left, so its queen takes row 2, column 5; indigo has one square left, so its queen takes row 1, column 2; blue has one square left, so its queen takes row 3, column 7; red has one square left, so its queen takes row 6, column 4; mint has one square left, so its queen takes row 4, column 3; slate has one square left, so its queen takes row 5, column 1; pale yellow has one square left, so its queen takes row 7, column 6. 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 7, column 6.
The board after step 11 — 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 #19
7x7 puzzle #19 is rated easy. 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.
Puzzle #19 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #19 are: mint (2 squares), blue (4 squares), amber (5 squares), slate (5 squares), red (6 squares), pale yellow (11 squares), indigo (16 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 16 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Mint has only 2 places to put its queen; indigo has 16. The spread between them on this board is 14 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Look at arrangement as well as area. Mint is the densest region on this grid at 100% of a 2×1 frame; red is the loosest, occupying only 60% of its 2×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Here is the full footprint of every color on puzzle #19, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Mint covers 2 squares, spanning 2 rows and 1 column (rows 4–5, columns 3–3). It sits wholly inside column 3, so its queen must be in that column.
Blue occupies 4 squares within rows 3–5, columns 6–7.
Amber: 5 squares across rows 1–2, columns 5–7.
Slate covers 5 squares, spanning 3 rows and 2 columns (rows 4–6, columns 1–2).
Red occupies 6 squares within rows 6–7, columns 1–5.
Pale yellow: 11 squares across rows 4–7, columns 4–7.
Indigo covers 16 squares, spanning 4 rows and 5 columns (rows 1–4, columns 1–5).
Where to start on this board
The most constrained color is where a solve should begin, and on #19 that is mint with 2 squares. It reaches from row 4 to row 5 and from column 3 to column 3 — 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 mint stays inside column 3, its queen belongs to that column and no other region may use it. Cross out the rest of column 3 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. Amber and red 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 #19
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 and 7 are the narrowest, touched by only 2 colors. Columns 1, 2, 3, 4, 6 and 7 are the tightest columns, with 3 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 6 rows. Row 4, meeting 5 colors, is the opposite case — the busiest line on #19 and the last one you should expect to crack.
Working through the middle game
The middle of #19 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.
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 #19 is rated easy
The rating reflects how much the board concedes up front. Puzzle #19 has one region confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 14 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.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #19 the place to look for one is around row 1.
Here is a shape check that gives nothing away: when #19 is solved, 4 queens sit on the outer edge of the grid and 3 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #19?
Puzzle #19 is rated easy. Its smallest color region holds 2 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 #19 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #19, 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 #19?
Start with the mint region — the most constrained color on this board, with 2 squares spanning rows 4–5 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.