10x10 Queens Puzzle #141
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.
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Step-by-step solution for puzzle #141
What follows is a complete solve of puzzle #141, 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 column.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 1, column 3 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 3, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The khaki region is down to one open square, at row 8, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 1, the remaining khaki squares, and the ring of neighbours around row 8, column 1.
Step 3. The amber region has 3 squares left, spread across rows 2 and 3, columns 5 and 6. 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 blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
The board after step 4 — 2 of 10 queens placed. Step 5. 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: 4 squares in all.
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: 6 squares come off.
Step 7. Wherever sea green 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.
Step 8. Every open square left in column 8 (5 open squares) belongs to the pale yellow region. Since that column must contain a queen, pale yellow is the colour that supplies it — so pale yellow squares anywhere else on the board are out, 6 squares in all.
Step 9. Column 7 has only slate squares left (2 open squares). The column needs a queen and only slate can provide one, which pins that colour to this column and kills its squares elsewhere: 4 squares.
The board after step 9 — 2 of 10 queens placed. Step 10. Column 9 now has exactly one open square, row 10, column 9, in the sea green region. Columns must each hold a queen, so that placement is forced. That clears row 10, column 9, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 11. Scan column 10 and only row 4, column 10 remains — a mint square. Every column takes a queen, so it takes this one. Cross out the whole of row 4 and column 10, the remaining mint squares, and the ring of neighbours around row 4, column 10.
Step 12. All of the slate region's remaining squares (2 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
Step 13. 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: pale yellow has one square left, so its queen takes row 7, column 8; slate has one square left, so its queen takes row 5, column 7; red has one square left, so its queen takes row 6, column 4; blue has one square left, so its queen takes row 3, column 2; orange has one square left, so its queen takes row 9, column 5; amber has one square left, so its queen takes row 2, column 6. 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 2, column 6.
The board after step 13 — 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 #141
Puzzle #141 is one of the hard-rated boards in the 10x10 set. Ten colors divide its 100 squares, and you win by placing ten queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
There is exactly one way to finish #141, 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 ten regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #141 are: indigo (1 square), khaki (1 square), sea green (3 squares), amber (8 squares), blue (10 squares), slate (10 squares), mint (14 squares), pale yellow (15 squares), red (16 squares), orange (22 squares). An even split would hand every color 10 squares, so the indigo region is running 9 squares under that average while the orange region is the roomiest area on the grid with 22 squares.
Every color takes one queen and one only, whatever its size — which is why the 21 square difference between indigo and orange 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.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and slate the most diffuse at 50% of its 5×4 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: 1 square across rows 1–1, columns 3–3. It never leaves row 1, so its queen is locked to that row.
Khaki covers 1 square, spanning 1 row and 1 column (rows 8–8, columns 1–1). It never leaves row 8, so its queen is locked to that row.
Sea green occupies 3 squares within rows 9–10, columns 9–10.
Amber: 8 squares across rows 1–3, columns 4–7.
Blue covers 10 squares, spanning 4 rows and 4 columns (rows 1–4, columns 1–4).
Slate occupies 10 squares within rows 4–8, columns 7–10.
Mint: 14 squares across rows 1–4, columns 6–10.
Pale yellow covers 15 squares, spanning 6 rows and 4 columns (rows 5–10, columns 6–9).
Red occupies 16 squares within rows 4–7, columns 1–5.
Orange: 22 squares across rows 5–10, columns 1–6.
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 1 square inside a 1×1 window running from row 1 to row 1 and column 3 to column 3. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Khaki and sea green 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 #141
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 3, 9 and 10 are the narrowest, touched by only 3 colors. Columns 2, 5, 8 and 10 are the tightest columns, with 3 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 9 rows. Row 8, meeting 4 colors, is the opposite case — the busiest line on #141 and the last one you should expect to crack.
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.
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 #141 is rated hard
Ratings track how generous the opening is. On #141 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 21-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.
Stuck on #141 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 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.
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 #141 is row 2.
Here is a shape check that gives nothing away: when #141 is solved, 4 queens sit on the outer edge of the grid and 6 sit inside it, and no queen lands 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 10x10 Queens puzzle #141?
Puzzle #141 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #141 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #141, 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 #141?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.