7x7 Queens Puzzle #146
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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #146
What follows is a complete solve of puzzle #146, 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 pairing argument on columns.
Techniques this board needs: region shadow, region confined to one line, pairing argument on columns, last square in a region, last square in a column, last square in a row.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Wherever amber ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. Blue is down to 4 candidates in rows 2–4, columns 1 and 2, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 3. Pale yellow cannot leave row 7 — every one of its open squares (3 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 5 squares in all.
The board after step 3 — 0 of 7 queens placed. Step 4. 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: 6 squares come off.
Step 5. Blue and red are now boxed into columns 1 and 2 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 2 squares at once.
Step 6. The indigo region has 5 squares left, spread across rows 1–3, columns 3–5. 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.
The board after step 6 — 0 of 7 queens placed. Step 7. Amber, mint, and pale yellow are now boxed into columns 5–7 and nothing else. That is 3 colours needing 3 columns, so they fill those columns between them — which locks every remaining colour out and removes 5 squares at once.
Step 8. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
Step 9. 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 7; column 2 is down to one square, putting a queen on row 6, column 2; row 5 is down to one square, putting a queen on row 5, column 4; indigo has one square left, so its queen takes row 1, column 3; mint has one square left, so its queen takes row 4, column 6; blue has one square left, so its queen takes row 3, column 1; pale yellow has one square left, so its queen takes row 7, column 5. 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 5.
The board after step 9 — 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 #146
Board #146 of the 7x7 bank carries a hard 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.
Puzzle #146 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 #146 are: amber (3 squares), pale yellow (3 squares), blue (4 squares), red (6 squares), indigo (7 squares), mint (9 squares), slate (17 squares). An even split would hand every color 7 squares, so the amber region is running 4 squares under that average while the slate region is the roomiest area on the grid with 17 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 amber, with 3 squares, is under far more pressure than slate with 17. A 14-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. Pale yellow is the tidiest shape on #146, packing 100% of its 1×3 bounding box, whereas indigo straggles across its 3×5 box at just 47%. 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 #146, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Amber occupies 3 squares within rows 1–2, columns 6–7.
Pale yellow: 3 squares across rows 7–7, columns 5–7. It never leaves row 7, so its queen is locked to that row.
Blue covers 4 squares, spanning 3 rows and 2 columns (rows 2–4, columns 1–2).
Red occupies 6 squares within rows 6–7, columns 1–4.
Indigo: 7 squares across rows 1–3, columns 1–5.
Mint covers 9 squares, spanning 5 rows and 3 columns (rows 2–6, columns 5–7).
Slate occupies 17 squares within rows 2–6, columns 1–6.
Where to start on this board
Begin where the choices are fewest. On this board that means amber, which owns just 3 squares inside a 2×2 window running from row 1 to row 2 and column 6 to column 7. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
With 2 rows and 2 columns of room, amber needs narrowing rather than solving outright. Test its 3 squares against the neighbours: a candidate that would strand another color is dead, and eliminating even two of them tightens the whole corner of the board around rows 1–2.
Work outward to the other flat regions next. Pale yellow 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 #146
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 5 and 7 are the narrowest, touched by only 2 colors. Columns 3, 4 and 7 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 6 rows. Row 2 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.
With seven queens to seat and seven regions competing over 49 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 7x7 boards quickly and players who stall halfway.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #146 is rated hard
The rating reflects how much the board concedes up front. Puzzle #146 has one region confined to a single row or column, its smallest color holds 3 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.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
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.
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 #146, start hunting for it near row 1.
A non-spoiling distribution check: solved, #146 carries 4 queens on the perimeter against 3 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 7x7 Queens puzzle #146?
Puzzle #146 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 #146 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #146, 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 #146?
Start with the amber region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 6–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.