10x10 Queens Puzzle #124
Difficulty: medium. 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 13-step reasoning is written out below.
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Step-by-step solution for puzzle #124
What follows is a complete solve of puzzle #124, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 10 queen placements and 3 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 region shadow.
Techniques this board needs: last square in a region, region confined to one line, region shadow.
Show the full walkthrough (10 steps) — contains the solution
Step 1. 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 2. The sea green region is down to one open square, at row 10, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 10, the remaining sea green squares, and the ring of neighbours around row 10, column 10.
Step 3. Only row 9, column 1 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 1, in orange and in the ring around that square is now dead.
The board after step 3 — 3 of 10 queens placed. Step 4. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.
Step 5. Only row 8, column 4 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 4, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 6. The pale yellow region is down to one open square, at row 7, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 2, the remaining pale yellow squares, and the ring of neighbours around row 7, column 2.
Step 7. Blue cannot leave column 3 — every one of its open squares (3 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 1 square in all.
The board after step 7 — 5 of 10 queens placed. Step 8. The mint region is down to one open square, at row 4, column 5. Every colour holds exactly one queen, so that square is forced. Row 4 and column 5 are now spoken for, along with the squares touching that queen.
Step 9. The slate region has 3 squares left, spread across rows 5 and 6, columns 7 and 9. 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 10. 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 7; slate has one square left, so its queen takes row 5, column 9; blue has one square left, so its queen takes row 3, column 3; indigo has one square left, so its queen takes row 1, 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 1, column 8.
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 #124
This is puzzle number 124 in the 10x10 collection, rated medium. The grid holds 100 squares split between ten colored regions, and a finished board carries ten queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
Puzzle #124 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #124 are: amber (1 square), sea green (1 square), orange (3 squares), indigo (8 squares), pale yellow (8 squares), khaki (14 squares), blue (15 squares), mint (15 squares), red (15 squares), slate (20 squares). An even split would hand every color 10 squares, so the amber region is running 9 squares under that average while the slate region is the roomiest area on the grid with 20 squares.
Every color takes one queen and one only, whatever its size — which is why the 19 square difference between amber and slate 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 amber is the most solid, filling 100% of its 1×1 box, and slate the most diffuse at 42% of its 8×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #124 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Amber covers 1 square, spanning 1 row and 1 column (rows 2–2, columns 6–6). It never leaves row 2, so its queen is locked to that row.
Sea green occupies 1 square within rows 10–10, columns 10–10. It never leaves row 10, so its queen is locked to that row.
Orange: 3 squares across rows 9–10, columns 1–2.
Indigo covers 8 squares, spanning 3 rows and 3 columns (rows 1–3, columns 8–10).
Pale yellow occupies 8 squares within rows 4–8, columns 1–3.
Khaki: 14 squares across rows 8–10, columns 2–8.
Blue covers 15 squares, spanning 6 rows and 4 columns (rows 1–6, columns 1–4).
Mint occupies 15 squares within rows 1–4, columns 3–7.
Red: 15 squares across rows 5–9, columns 4–8.
Slate covers 20 squares, spanning 8 rows and 6 columns (rows 3–10, columns 5–10).
Where to start on this board
Amber is the natural opening on #124: it is the smallest region on the grid at 1 square, boxed into rows 2–2 and columns 6–6. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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. Sea green and orange 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 #124
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 7 are the narrowest, touched by only 3 colors. Column 9 is the tightest column, with 2 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 9 rows. By contrast row 10 meets 4 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
With ten queens to seat and ten regions competing over 100 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 10x10 boards quickly and players who stall halfway.
Resist the plausible-looking queen. On #124 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #124 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers four single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 19. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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 #124 is column 9.
As a sanity check rather than a spoiler: the finished solution to #124 puts 3 queens on the outer border and 7 queens in the interior, 1 of them in an actual corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 #124?
Puzzle #124 is rated medium. 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 #124 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #124, 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 #124?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.