7x7 Queens Puzzle #5
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 10-step reasoning is written out below.
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Step-by-step solution for puzzle #5
What follows is a complete solve of puzzle #5, worked the way a person works it rather than the way a computer does. It runs to 10 deductions — 7 queen placements and 3 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 confined to one line, region shadow, last square in a region, last square in a row.
Show the full walkthrough (5 steps) — contains the solution
Step 1. 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: 7 squares in all.
Step 2. Blue is down to 6 candidates in rows 3–5, columns 1–3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 3. Only row 4, column 3 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 3, in mint and in the ring around that square is now dead.
The board after step 3 — 1 of 7 queens placed. Step 4. All of the blue 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 5. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: pale yellow has one square left, so its queen takes row 7, column 2; red has one square left, so its queen takes row 6, column 4; row 2 is down to one square, putting a queen on row 2, column 5; indigo has one square left, so its queen takes row 1, column 7; slate has one square left, so its queen takes row 5, column 6; blue has one square left, so its queen takes row 3, 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 3, column 1.
The board after step 5 — 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 #5
Puzzle #5 is one of the easy-rated boards in the 7x7 set. Seven colors divide its 49 squares, and you win by placing seven queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
As with every puzzle in this collection, #5 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 #5 are: indigo (2 squares), mint (2 squares), pale yellow (4 squares), blue (6 squares), slate (8 squares), red (8 squares), amber (19 squares). An even split would hand every color 7 squares, so the indigo region is running 5 squares under that average while the amber region is the roomiest area on the grid with 19 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 indigo, with 2 squares, is under far more pressure than amber with 19. A 17-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. Indigo is the tidiest shape on #5, packing 100% of its 1×2 bounding box, whereas red straggles across its 3×6 box at just 44%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Here is the full footprint of every color on puzzle #5, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo occupies 2 squares within rows 1–1, columns 6–7. It never leaves row 1, so its queen is locked to that row.
Mint: 2 squares across rows 4–4, columns 2–3. It never leaves row 4, so its queen is locked to that row.
Pale yellow covers 4 squares, spanning 2 rows and 3 columns (rows 6–7, columns 1–3).
Blue occupies 6 squares within rows 3–5, columns 1–3.
Slate: 8 squares across rows 4–6, columns 5–7.
Red covers 8 squares, spanning 3 rows and 6 columns (rows 5–7, columns 2–7).
Amber occupies 19 squares within rows 1–4, columns 1–7.
Where to start on this board
Indigo is the natural opening on #5: it is the smallest region on the grid at 2 squares, boxed into rows 1–1 and columns 6–7. Since one of those squares must hold a queen, that block of 1 row and 2 columns is the most contested part of the board.
Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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.
Work outward to the other flat regions next. Mint and pale yellow 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 #5
A quick way to find the next move is to count how many different colors touch each line. On this board, row 2 is the narrowest, touched by only 1 color. Column 4 is the tightest column, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 1 color, so one of that handful must take the row and the rest are squeezed into the other 6 rows. Row 4 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
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
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 #5 is rated easy
The rating reflects how much the board concedes up front. Puzzle #5 has two regions confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 1 color, and the gap between its largest and smallest regions is 17 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
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.
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 #5, start hunting for it near row 2.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 4 queens in the middle, including 1 in a corner. 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.
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Questions about this puzzle
How hard is 7x7 Queens puzzle #5?
Puzzle #5 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 1 color, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #5 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #5, 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 #5?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–1 and columns 6–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.