10x10 Queens Puzzle #70
Difficulty: hard. Place 10 queens on this 10x10 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 18-step reasoning is written out below.
Previous puzzle · All 10x10 puzzles · Next puzzle
Step-by-step solution for puzzle #70
What follows is a complete solve of puzzle #70, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 10 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 line confined to one region.
Techniques this board needs: last square in a region, region shadow, region confined to one line, line confined to one region, last square in a row, last square in a column.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 5, column 2 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 2, the rest of the slate region and every square adjacent to it — diagonals included.
Step 2. Amber is down to 3 candidates in rows 1 and 2, columns 9 and 10, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The blue region has 5 squares left, spread across rows 3, 7, 8, 9, and 10, columns 1 and 3. 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 4. All of the pale yellow region's remaining squares (3 open squares) lie in column 10. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
Step 5. Only row 2, column 9 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 9, the rest of the amber region and every square adjacent to it — diagonals included.
The board after step 5 — 2 of 10 queens placed. Step 6. All of the mint region's remaining squares (2 open squares) lie in row 4. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 7. Wherever sea green 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 8. Every open square left in row 1 (6 open squares) belongs to the indigo region. Since that row must contain a queen, indigo is the colour that supplies it — so indigo squares anywhere else on the board are out, 3 squares in all.
Step 9. Look along row 3: one square survives, row 3, column 3, which belongs to blue. A row cannot be left empty, so the queen goes there. Everything else in row 3, in column 3, in blue and in the ring around that square is now dead.
The board after step 9 — 3 of 10 queens placed. Step 10. The sea green region is down to one open square, at row 10, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 4, the remaining sea green squares, and the ring of neighbours around row 10, column 4.
Step 11. Scan column 1 and only row 1, column 1 remains — a indigo square. Every column takes a queen, so it takes this one. Cross out the whole of row 1 and column 1, the remaining indigo squares, and the ring of neighbours around row 1, column 1.
Step 12. The khaki region has 6 squares left, spread across rows 7–9, columns 5–8. 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 13. Orange cannot leave column 8 — every one of its open squares (3 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 2 squares in all.
Step 14. 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: mint has one square left, so its queen takes row 4, column 7; row 8 is down to one square, putting a queen on row 8, column 5; red has one square left, so its queen takes row 6, column 6; pale yellow has one square left, so its queen takes row 7, column 10; orange has one square left, so its queen takes row 9, column 8. 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 9, column 8.
The board after step 14 — 10 of 10 queens placed.
That completes the board: 10 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 10x10 Queens puzzle #70
Board #70 of the 10x10 bank carries a hard rating. Its 100 squares are shared between ten colored regions, and the solution places ten 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, #70 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 #70 are: slate (1 square), amber (3 squares), pale yellow (6 squares), sea green (7 squares), red (10 squares), mint (11 squares), blue (14 squares), orange (14 squares), indigo (17 squares), khaki (17 squares). An even split would hand every color 10 squares, so the slate region is running 9 squares under that average while the khaki region is the roomiest area on the grid with 17 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Slate has only 1 place to put its queen; khaki has 17. 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.
Square count is only half the story — how a color is arranged counts too. Slate is the tidiest shape on #70, packing 100% of its 1×1 bounding box, whereas khaki straggles across its 7×6 box at just 40%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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 covers 1 square, spanning 1 row and 1 column (rows 5–5, columns 2–2). It never leaves row 5, so its queen is locked to that row.
Amber occupies 3 squares within rows 1–2, columns 9–10.
Pale yellow: 6 squares across rows 3–7, columns 9–10.
Sea green covers 7 squares, spanning 4 rows and 3 columns (rows 7–10, columns 2–4).
Red occupies 10 squares within rows 4–8, columns 5–7.
Mint: 11 squares across rows 1–4, columns 5–9.
Blue covers 14 squares, spanning 8 rows and 3 columns (rows 3–10, columns 1–3).
Orange occupies 14 squares within rows 5–10, columns 7–10.
Indigo: 17 squares across rows 1–3, columns 1–7.
Khaki covers 17 squares, spanning 7 rows and 6 columns (rows 4–10, columns 3–8).
Where to start on this board
The most constrained color is where a solve should begin, and on #70 that is slate with 1 square. It reaches from row 5 to row 5 and from column 2 to column 2 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. Then look at which colors just lost ground: on a grid this size that one observation usually forces a second region within a move or two.
Work outward to the other flat regions next. Amber 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 #70
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 2 are the narrowest, touched by only 3 colors. Column 1 is the tightest column, with 2 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 9 rows. Row 7 is the crowded extreme at 6 colors — worth revisiting later, not now.
Working through the middle game
The middle of #70 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
The whole middle game reduces to two sweeps. Sweep the ten colors looking for one with a single square left; sweep the ten rows and ten columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 10x10 solve from a stalled one.
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 #70 is rated hard
Ratings track how generous the opening is. On #70 you get two regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 16-square gap between the largest and smallest regions. Those four numbers largely explain the hard 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 hard 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 10x10
At 10x10 a full re-scan after every move starts to get slow, so work locally instead. Once a queen goes down, check only the regions, rows and columns that placement actually touched — that is where new information appeared. Fall back to a complete sweep only when the local pass turns up nothing, and your solve times will drop noticeably.
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 #70 the place to look for one is around column 1.
A non-spoiling distribution check: solved, #70 carries 3 queens on the perimeter against 7 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 10x10 Queens puzzle #70?
Puzzle #70 is rated hard. Its smallest color region holds 1 square, 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 10x10 puzzle #70 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #70, has been verified to have exactly one valid arrangement of ten queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #70?
Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 2–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.