7x7 Queens Puzzle #106
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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #106
What follows is a complete solve of puzzle #106, 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 region shadow.
Techniques this board needs: region confined to one line, region shadow, last square in a region.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Indigo cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to indigo, so every square in it owned by another colour is dead: 7 squares in all.
Step 2. Amber is down to 6 candidates in rows 2–5, columns 2–4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The slate region has 3 squares left, spread across rows 5 and 6, columns 2 and 3. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 4. Wherever red ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
The board after step 4 — 0 of 7 queens placed. Step 5. Slate cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 2 squares in all.
Step 6. The amber region has 3 squares left, spread across rows 2 and 4, columns 3 and 4. 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 7. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 4 squares in all.
Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: red has one square left, so its queen takes row 6, column 4; slate has one square left, so its queen takes row 5, column 2; amber has one square left, so its queen takes row 2, column 3; indigo has one square left, so its queen takes row 1, 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 1, column 1.
The board after step 8 — 4 of 7 queens placed. Step 9. The blue region has 3 squares left, spread across rows 3 and 4, columns 5 and 6. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 10. Only row 4, column 7 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 7, the rest of the mint region and every square adjacent to it — diagonals included.
Step 11. 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. Cross out the whole of row 3 and column 5, the remaining blue squares, and the ring of neighbours around row 3, column 5.
Step 12. 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.
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 #106
Board #106 of the 7x7 bank carries a easy 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.
Like every board on this site, #106 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #106 are: indigo (2 squares), pale yellow (3 squares), red (4 squares), slate (6 squares), amber (10 squares), mint (11 squares), blue (13 squares). An even split would hand every color 7 squares, so the indigo region is running 5 squares under that average while the blue region is the roomiest area on the grid with 13 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 blue with 13. A 11-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 2×1 frame; amber is the loosest, occupying only 50% of its 5×4 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 easy board.
Indigo covers 2 squares, spanning 2 rows and 1 column (rows 1–2, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Pale yellow occupies 3 squares within rows 7–7, columns 5–7. It never leaves row 7, so its queen is locked to that row.
Red: 4 squares across rows 6–7, columns 2–4.
Slate covers 6 squares, spanning 3 rows and 3 columns (rows 5–7, columns 1–3).
Amber occupies 10 squares within rows 1–5, columns 1–4.
Mint: 11 squares across rows 2–6, columns 4–7.
Blue covers 13 squares, spanning 4 rows and 5 columns (rows 1–4, columns 3–7).
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 2 squares inside a 2×1 window running from row 1 to row 2 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because indigo stays inside column 1, its queen belongs to that column and no other region may use it. Cross out the rest of column 1 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 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 #106
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3, 4, 5, 6 and 7 are the narrowest, touched by only 3 colors. Columns 1, 2, 5, 6 and 7 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 3 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 4 colors — worth revisiting later, not now.
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.
Keep alternating between two views of the board. In the region view you ask which of the seven colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 7x7 board unwinds.
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 #106 is rated easy
The easy label comes out of four measurable things about #106: two of its regions are locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 3 colors, and its largest and smallest regions differ by 11. 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.
If #106 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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 #106, start hunting for it near row 1.
A non-spoiling distribution check: solved, #106 carries 3 queens on the perimeter against 4 queens inside, 1 of them cornered. 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 #106?
Puzzle #106 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #106 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #106, 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 #106?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–2 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.