10x10 Queens Puzzle #83
Difficulty: easy. 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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #83
What follows is a complete solve of puzzle #83, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 10 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 rows.
Techniques this board needs: region shadow, region confined to one line, pairing argument on rows, last square in a region, last square in a column.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Wherever orange ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 2. Sea green is down to 3 candidates in rows 9 and 10, columns 8 and 9, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about sea green itself.
Step 3. Khaki cannot leave column 10 — 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.
The board after step 3 — 0 of 10 queens placed. Step 4. Here is the pairing argument. The orange and sea green regions have no open squares outside rows 9 and 10 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 9 squares come off in one stroke.
Step 5. Only row 8, column 10 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 10, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 6. The red region has 4 squares left, spread across rows 6 and 7, columns 6–8. 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 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: 8 squares in all.
The board after step 7 — 1 of 10 queens placed. 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 8; sea green has one square left, so its queen takes row 10, column 9; orange has one square left, so its queen takes row 9, column 3; pale yellow has one square left, so its queen takes row 7, column 2. 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 7, column 2.
Step 9. All of the indigo 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 10. 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 6; indigo has one square left, so its queen takes row 1, column 7; column 5 is down to one square, putting a queen on row 5, column 5; mint has one square left, so its queen takes row 4, column 1; amber has one square left, so its queen takes row 2, 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 2, column 4.
The board after step 10 — 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 #83
10x10 puzzle #83 is rated easy. Ten colored regions cover its 100 squares, and your job is to seat ten queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
As with every puzzle in this collection, #83 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 #83 are: sea green (3 squares), khaki (4 squares), orange (4 squares), indigo (8 squares), mint (8 squares), slate (12 squares), red (14 squares), pale yellow (14 squares), blue (15 squares), amber (18 squares). An even split would hand every color 10 squares, so the sea green region is running 7 squares under that average while the amber region is the roomiest area on the grid with 18 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Sea green has only 3 places to put its queen; amber has 18. The spread between them on this board is 15 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. Mint is the tidiest shape on #83, packing 80% of its 5×2 bounding box, whereas red straggles across its 5×6 box at just 47%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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.
Sea green occupies 3 squares within rows 9–10, columns 8–9.
Khaki: 4 squares across rows 8–10, columns 9–10.
Orange covers 4 squares, spanning 2 rows and 3 columns (rows 9–10, columns 1–3).
Indigo occupies 8 squares within rows 1–3, columns 7–10.
Mint: 8 squares across rows 3–7, columns 1–2.
Slate covers 12 squares, spanning 4 rows and 4 columns (rows 4–7, columns 3–6).
Red occupies 14 squares within rows 6–10, columns 5–10.
Pale yellow: 14 squares across rows 7–10, columns 1–6.
Blue covers 15 squares, spanning 5 rows and 5 columns (rows 2–6, columns 6–10).
Amber occupies 18 squares within rows 1–4, columns 1–6.
Where to start on this board
Open on the tightest color. Here that is sea green, confined to 3 squares between rows 9 and 10 and columns 8 and 9. Its queen has nowhere else to go, which means those 2 rows and 2 columns carry more constraint than anywhere else on #83.
Sea green spans 2 rows, so it stays open for now — but it is still the shortest list on the board at 3 squares. Work through those squares first and mark the ones that would leave another region homeless. That pruning is what makes the rest of the grid legible.
Work outward to the other flat regions next. Orange 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 #83
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Columns 4 and 7 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 9 rows. Row 10 is the crowded extreme at 5 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.
Two checks, run alternately, will carry you through the 100 squares of this grid. First: has any of the ten regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 10x10 boards almost always run one of those checks and forget the other.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #83 is rated easy
The easy label comes out of four measurable things about #83: it has no region locked to one row or column, its smallest color spans 3 squares, its least crowded row meets 2 colors, and its largest and smallest regions differ by 15. Boards that score tight on those measures give up their first queen fast.
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 easy 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 #83 the place to look for one is around row 1.
A non-spoiling distribution check: solved, #83 carries 4 queens on the perimeter against 6 queens inside, with the corners empty. 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 10x10 Queens puzzle #83?
Puzzle #83 is rated easy. Its smallest color region holds 3 squares, its tightest row is touched by 2 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 10x10 puzzle #83 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #83, 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 #83?
Start with the sea green region — the most constrained color on this board, with 3 squares spanning rows 9–10 and columns 8–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.