8x8 Queens Puzzle #122
Difficulty: medium. Place 8 queens on this 8x8 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 22-step reasoning is written out below.
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Step-by-step solution for puzzle #122
What follows is a complete solve of puzzle #122, worked the way a person works it rather than the way a computer does. It runs to 22 deductions — 8 queen placements and 14 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 proof by contradiction.
Techniques this board needs: region shadow, region confined to one line, pairing argument on rows, pairing argument on columns, line confined to one region, proof by contradiction, last square in a region.
Show the full walkthrough (17 steps) — contains the solution
Step 1. Wherever indigo 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.
Step 2. Red is down to 4 candidates in rows 6–8, columns 1 and 2, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about red itself.
Step 3. Khaki cannot leave column 3 — every one of its open squares (3 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 7 squares in all.
Step 4. Wherever red 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.
The board after step 4 — 0 of 8 queens placed. Step 5. Red, pale yellow, and khaki are now boxed into rows 6–8 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 10 squares at once.
Step 6. Here is the pairing argument. The blue and red regions have no open squares outside columns 1 and 2 — 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 7. Mint cannot leave column 4 — 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: 5 squares in all.
Step 8. Every open square left in column 5 (3 open squares) belongs to the amber region. Since that column must contain a queen, amber is the colour that supplies it — so amber squares anywhere else on the board are out, 3 squares in all.
Step 9. Test row 1, column 7 for indigo: place a queen there, run the forced consequences through, and column 2 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
The board after step 9 — 0 of 8 queens placed. Step 10. Wherever indigo ends up among its 2 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 11. Test row 2, column 7 for indigo: place a queen there, run the forced consequences through, and column 2 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 12. The indigo region is down to one open square, at row 1, column 8. Every colour holds exactly one queen, so that square is forced. Row 1 and column 8 are now spoken for, along with the squares touching that queen.
Step 13. Test row 3, column 5 for amber: place a queen there, run the forced consequences through, and the red region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
The board after step 13 — 1 of 8 queens placed. Step 14. The amber region is down to one open square, at row 2, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 5, the remaining amber squares, and the ring of neighbours around row 2, column 5.
Step 15. Test row 4, column 1 for blue: place a queen there, run the forced consequences through, and row 7 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 16. Now a short proof by contradiction. Suppose the blue queen went to row 4, column 2. Follow the forced moves that would create and row 6 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 17. 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: blue has one square left, so its queen takes row 3, column 1; red has one square left, so its queen takes row 6, column 2; khaki has one square left, so its queen takes row 8, column 3; pale yellow has one square left, so its queen takes row 7, column 7; slate has one square left, so its queen takes row 5, column 6; mint has one square left, so its queen takes row 4, column 4. 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 4, column 4.
The board after step 17 — 8 of 8 queens placed.
That completes the board: 8 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 8x8 Queens puzzle #122
Board #122 of the 8x8 bank carries a medium rating. Its 64 squares are shared between eight colored regions, and the solution places eight queens: one per row, one per column, one per region, none of them side by side or corner to corner.
As with every puzzle in this collection, #122 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 #122 are: indigo (3 squares), red (4 squares), pale yellow (4 squares), khaki (4 squares), mint (8 squares), blue (9 squares), amber (13 squares), slate (19 squares). An even split would hand every color 8 squares, so the indigo region is running 5 squares under that average while the slate region is the roomiest area on the grid with 19 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 3 places to put its queen; slate has 19. The spread between them on this board is 16 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
A region's outline can constrain it more than its size does. Here amber is the most solid, filling 81% of its 4×4 box, and slate the most diffuse at 54% of its 7×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
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.
Indigo occupies 3 squares within rows 1–2, columns 7–8.
Red: 4 squares across rows 6–8, columns 1–2.
Pale yellow covers 4 squares, spanning 2 rows and 3 columns (rows 7–8, columns 6–8).
Khaki occupies 4 squares within rows 6–8, columns 2–3.
Mint: 8 squares across rows 3–6, columns 2–4.
Blue covers 9 squares, spanning 6 rows and 2 columns (rows 1–6, columns 1–2).
Amber occupies 13 squares within rows 1–4, columns 3–6.
Slate: 19 squares across rows 2–8, columns 4–8.
Where to start on this board
Indigo is the natural opening on #122: it is the smallest region on the grid at 3 squares, boxed into rows 1–2 and columns 7–8. Since one of those squares must hold a queen, that block of 2 rows and 2 columns is the most contested part of the board.
With 2 rows and 2 columns of room, indigo 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 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 #122
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 3 colors. Columns 1 and 5 are the tightest columns, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 7 rows. Row 6, meeting 5 colors, is the opposite case — the busiest line on #122 and the last one you should expect to crack.
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.
Keep alternating between two views of the board. In the region view you ask which of the eight 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 8x8 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 #122 is rated medium
Ratings track how generous the opening is. On #122 you get no region pinned to a single row or column, a smallest color of 3 squares, a tightest row crossed by 3 colors, and a 16-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.
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 medium 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 8x8
At 8x8 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 #122 the place to look for one is around column 1.
Here is a shape check that gives nothing away: when #122 is solved, 3 queens sit on the outer edge of the grid and 5 sit inside it, with 1 queen 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 8x8 Queens puzzle #122?
Puzzle #122 is rated medium. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 8x8 puzzle #122 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #122, has been verified to have exactly one valid arrangement of eight queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #122?
Start with the indigo region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 7–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.