10x10 Queens Puzzle #214
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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #214
What follows is a complete solve of puzzle #214, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 10 queen placements and 11 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 confined to one line, region shadow, pairing argument on rows, last square in a region.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Indigo cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to indigo, so every square in it owned by another colour is dead: 12 squares in all.
Step 2. All of the blue region's remaining squares (3 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 3. The slate region has 4 squares left, spread across rows 4 and 5, columns 7–9. 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 4. Wherever red 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.
The board after step 4 — 0 of 10 queens placed. Step 5. Slate is down to 3 candidates in rows 4 and 5, columns 7 and 8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
Step 6. All of the orange region's remaining squares (6 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
Step 7. Blue cannot leave row 3 — every one of its open squares (2 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 3 squares in all.
Step 8. Here is the pairing argument. The indigo and amber regions have no open squares outside rows 1 and 2 — 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: 7 squares come off in one stroke.
Step 9. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 5 squares in all.
The board after step 9 — 0 of 10 queens placed. Step 10. All of the slate region's remaining squares (2 open squares) lie in row 5. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 11. Only row 6, column 10 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 10, in red and in the ring around that square is now dead.
Step 12. 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: 7 squares come off.
Step 13. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: khaki has one square left, so its queen takes row 8, column 8; slate has one square left, so its queen takes row 5, column 7; mint has one square left, so its queen takes row 4, column 5; 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 2; amber has one square left, so its queen takes row 2, column 9; pale yellow has one square left, so its queen takes row 7, column 6; orange has one square left, so its queen takes row 9, column 1; sea green has one square left, so its queen takes row 10, 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 10, column 4.
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 #214
Board #214 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.
Like every board on this site, #214 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #214 are: indigo (2 squares), slate (4 squares), red (5 squares), orange (6 squares), blue (8 squares), amber (9 squares), pale yellow (10 squares), khaki (10 squares), mint (15 squares), sea green (31 squares). An even split would hand every color 10 squares, so the indigo region is running 8 squares under that average while the sea green region is the roomiest area on the grid with 31 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 indigo, with 2 squares, is under far more pressure than sea green with 31. A 29-square gap like this one rewards players who start where the choices are fewest.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 2×1 box that encloses it, while blue is the most scattered at 40% of its 5×4 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
Region by region
Here is the full footprint of every color on puzzle #214, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo covers 2 squares, spanning 2 rows and 1 column (rows 1–2, columns 2–2). It sits wholly inside column 2, so its queen must be in that column.
Slate occupies 4 squares within rows 4–5, columns 7–9.
Red: 5 squares across rows 4–6, columns 8–10.
Orange covers 6 squares, spanning 6 rows and 1 column (rows 4–9, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Blue occupies 8 squares within rows 1–5, columns 1–4.
Amber: 9 squares across rows 1–3, columns 7–10.
Pale yellow covers 10 squares, spanning 4 rows and 5 columns (rows 4–7, columns 3–7).
Khaki occupies 10 squares within rows 6–10, columns 7–10.
Mint: 15 squares across rows 1–4, columns 3–8.
Sea green covers 31 squares, spanning 5 rows and 9 columns (rows 6–10, columns 1–9).
Where to start on this board
The most constrained color is where a solve should begin, and on #214 that is indigo with 2 squares. It reaches from row 1 to row 2 and from column 2 to column 2 — 2 rows 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 indigo stays inside column 2, its queen belongs to that column and no other region may use it. Cross out the rest of column 2 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. Slate 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 #214
A quick way to find the next move is to count how many different colors touch each line. On this board, row 10 is the narrowest, touched by only 2 colors. Columns 1, 2, 5, 6 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 2 colors has to be claimed by one of them, which pushes every remaining region into the other 9 rows. Row 4, meeting 6 colors, is the opposite case — the busiest line on #214 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.
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.
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 #214 is rated hard
The rating reflects how much the board concedes up front. Puzzle #214 has two regions confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 29 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
If #214 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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.
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 #214, start hunting for it near row 10.
Here is a shape check that gives nothing away: when #214 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 #214?
Puzzle #214 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #214 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #214, 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 #214?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–2 and columns 2–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.