8x8 Queens Puzzle #173
Difficulty: hard. 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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #173
What follows is a complete solve of puzzle #173, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 8 queen placements and 7 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.
Show the full walkthrough (11 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 slate region's remaining squares (2 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 10 squares come off.
Step 3. The red region has 4 squares left, spread across rows 5–7, columns 4 and 5. 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 mint ends up among its 6 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. Pale yellow is down to 2 candidates in rows 7 and 8, columns 1 and 2, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 6. Here is the pairing argument. The mint and pale yellow 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: 5 squares come off in one stroke.
Step 7. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 4; slate has one square left, so its queen takes row 5, column 3; mint has one square left, so its queen takes row 4, column 1; 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 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 6, column 5.
The board after step 7 — 5 of 8 queens placed. Step 8. The indigo region has 3 squares left, spread across rows 1 and 2, columns 7 and 8. 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 9. Only row 2, column 6 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 6, the rest of the amber region and every square adjacent to it — diagonals included.
Step 10. 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. Cross out the whole of row 1 and column 8, the remaining indigo squares, and the ring of neighbours around row 1, column 8.
Step 11. Only row 8, column 7 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 7, in khaki and in the ring around that square is now dead.
The board after step 11 — 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 #173
Puzzle #173 is one of the hard-rated boards in the 8x8 set. Eight colors divide its 64 squares, and you win by placing eight 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, #173 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 #173 are: slate (2 squares), pale yellow (3 squares), indigo (4 squares), red (5 squares), blue (10 squares), mint (12 squares), amber (14 squares), khaki (14 squares). An even split would hand every color 8 squares, so the slate region is running 6 squares under that average while the khaki region is the roomiest area on the grid with 14 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 slate, with 2 squares, is under far more pressure than khaki with 14. A 12-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Slate is the densest region on this grid at 100% of a 2×1 frame; mint is the loosest, occupying only 50% of its 6×4 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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.
Slate occupies 2 squares within rows 4–5, columns 3–3. It sits wholly inside column 3, so its queen must be in that column.
Pale yellow: 3 squares across rows 7–8, columns 1–2.
Indigo covers 4 squares, spanning 3 rows and 2 columns (rows 1–3, columns 7–8).
Red occupies 5 squares within rows 5–7, columns 4–5.
Blue: 10 squares across rows 1–4, columns 1–4.
Mint covers 12 squares, spanning 6 rows and 4 columns (rows 3–8, columns 1–4).
Amber occupies 14 squares within rows 1–4, columns 4–8.
Khaki: 14 squares across rows 5–8, columns 4–8.
Where to start on this board
Open on the tightest color. Here that is slate, confined to 2 squares between rows 4 and 5 and columns 3 and 3. Its queen has nowhere else to go, which means those 2 rows and 1 column carry more constraint than anywhere else on #173.
Because slate stays inside column 3, its queen belongs to that column and no other region may use it. Cross out the rest of column 3 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 #173
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 6 and 8 are the narrowest, touched by only 3 colors. Column 6 is the tightest column, 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 7, meeting 4 colors, is the opposite case — the busiest line on #173 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.
The whole middle game reduces to two sweeps. Sweep the eight colors looking for one with a single square left; sweep the eight rows and eight columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 8x8 solve from a stalled one.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #173 is rated hard
Ratings track how generous the opening is. On #173 you get one region pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 3 colors, and a 12-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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.
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.
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 #173, start hunting for it near column 6.
Here is a shape check that gives nothing away: when #173 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 #173?
Puzzle #173 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 8x8 puzzle #173 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #173, 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 #173?
Start with the slate region — the most constrained color on this board, with 2 squares spanning rows 4–5 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.