7x7 Queens Puzzle #148
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 13-step reasoning is written out below.
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Step-by-step solution for puzzle #148
What follows is a complete solve of puzzle #148, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 7 queen placements and 6 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 shadow, region confined to one line, last square in a region.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Wherever indigo 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.
Step 2. All of the blue region's remaining squares (2 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 9 squares come off.
Step 3. Only row 7, column 6 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 6, in pale yellow and in the ring around that square is now dead.
Step 4. The indigo region is down to one open square, at row 1, column 7. Every colour holds exactly one queen, so that square is forced. Row 1 and column 7 are now spoken for, along with the squares touching that queen.
The board after step 4 — 2 of 7 queens placed. Step 5. Amber is down to 3 candidates in rows 2 and 3, columns 2 and 3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 6. All of the mint 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: 4 squares come off.
Step 7. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 1 square in all.
Step 8. The blue region is down to one open square, at row 3, column 5. Every colour holds exactly one queen, so that square is forced. Row 3 and column 5 are now spoken for, along with the squares touching that queen.
Step 9. Only row 4, column 1 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 1, the rest of the mint region and every square adjacent to it — diagonals included.
The board after step 9 — 4 of 7 queens placed. Step 10. All of the slate region's remaining squares (2 open squares) lie in column 4. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
Step 11. Only row 6, column 2 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 2, in red and in the ring around that square is now dead.
Step 12. The amber region is down to one open square, at row 2, column 3. Every colour holds exactly one queen, so that square is forced. Row 2 and column 3 are now spoken for, along with the squares touching that queen.
Step 13. Only row 5, column 4 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 4, the rest of the slate region and every square adjacent to it — diagonals included.
The board after step 13 — 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 #148
This is puzzle number 148 in the 7x7 collection, rated hard. The grid holds 49 squares split between seven colored regions, and a finished board carries seven queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
There is exactly one way to finish #148, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these seven regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #148 are: blue (2 squares), mint (3 squares), pale yellow (3 squares), indigo (4 squares), amber (9 squares), red (10 squares), slate (18 squares). An even split would hand every color 7 squares, so the blue region is running 5 squares under that average while the slate region is the roomiest area on the grid with 18 squares.
Every color takes one queen and one only, whatever its size — which is why the 16 square difference between blue and slate is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Shape matters as much as size. The blue region is the most compact color here, filling 100% of the 2×1 box that encloses it, while slate is the most scattered at 60% of its 6×5 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Blue covers 2 squares, spanning 2 rows and 1 column (rows 2–3, columns 5–5). It sits wholly inside column 5, so its queen must be in that column.
Mint occupies 3 squares within rows 2–4, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Pale yellow: 3 squares across rows 6–7, columns 5–6.
Indigo covers 4 squares, spanning 3 rows and 2 columns (rows 1–3, columns 6–7).
Amber occupies 9 squares within rows 1–3, columns 1–5.
Red: 10 squares across rows 4–7, columns 1–3.
Slate covers 18 squares, spanning 6 rows and 5 columns (rows 2–7, columns 3–7).
Where to start on this board
Open on the tightest color. Here that is blue, confined to 2 squares between rows 2 and 3 and columns 5 and 5. Its queen has nowhere else to go, which means those 2 rows and 1 column carry more constraint than anywhere else on #148.
Because blue stays inside column 5, its queen belongs to that column and no other region may use it. Cross out the rest of column 5 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. Pale yellow 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 #148
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 5 are the narrowest, touched by only 2 colors. Columns 2, 4 and 7 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 3 sits at the far end with 5 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 #148 is rated hard
Ratings track how generous the opening is. On #148 you get two regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 16-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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.
Stuck on #148 despite the hard rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #148 is row 1.
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 #148?
Puzzle #148 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #148 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #148, 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 #148?
Start with the blue region — the most constrained color on this board, with 2 squares spanning rows 2–3 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.