12x12 Queens Puzzle #26
Difficulty: hard. Place 12 queens on this 12x12 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 #26
What follows is a complete solve of puzzle #26, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 12 queen placements and 6 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 columns.
Techniques this board needs: region shadow, last square in a region, region confined to one line, pairing argument on columns.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Wherever indigo 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 2. 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: blue has one square left, so its queen takes row 3, column 11; indigo has one square left, so its queen takes row 1, column 10; slate has one square left, so its queen takes row 5, column 12; pale yellow has one square left, so its queen takes row 7, column 9. 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 9.
Step 3. All of the amber region's remaining squares (3 open squares) lie in row 2. 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 3 — 4 of 12 queens placed. Step 4. Mint cannot leave row 4 — every one of its open squares (3 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 5 squares in all.
Step 5. The red region is down to one open square, at row 6, column 7. Every colour holds exactly one queen, so that square is forced. Row 6 and column 7 are now spoken for, along with the squares touching that queen.
Step 6. The orange region has 4 squares left, spread across rows 9–11, columns 1 and 2. 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.
The board after step 6 — 5 of 12 queens placed. Step 7. All of the rose region's remaining squares (2 open squares) lie in row 12. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 8. Orange and rose are now boxed into columns 1 and 2 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 4 squares at once.
Step 9. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: mint has one square left, so its queen takes row 4, column 3; sea green has one square left, so its queen takes row 10, column 4; orange has one square left, so its queen takes row 9, column 1; teal has one square left, so its queen takes row 11, column 8; amber has one square left, so its queen takes row 2, column 6; khaki has one square left, so its queen takes row 8, column 5; rose has one square left, so its queen takes row 12, 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 12, column 2.
The board after step 9 — 12 of 12 queens placed.
That completes the board: 12 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 12x12 Queens puzzle #26
Board #26 of the 12x12 bank carries a hard rating. Its 144 squares are shared between twelve colored regions, and the solution places twelve 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, #26 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 #26 are: blue (2 squares), rose (3 squares), indigo (4 squares), orange (4 squares), slate (8 squares), pale yellow (10 squares), red (14 squares), sea green (14 squares), amber (15 squares), mint (18 squares), khaki (22 squares), teal (30 squares). An even split would hand every color 12 squares, so the blue region is running 10 squares under that average while the teal region is the roomiest area on the grid with 30 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 blue, with 2 squares, is under far more pressure than teal with 30. A 28-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Blue is the densest region on this grid at 100% of a 2×1 frame; sea green is the loosest, occupying only 50% of its 7×4 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Here is the full footprint of every color on puzzle #26, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Blue occupies 2 squares within rows 2–3, columns 11–11. It sits wholly inside column 11, so its queen must be in that column.
Rose: 3 squares across rows 11–12, columns 1–2.
Indigo covers 4 squares, spanning 3 rows and 2 columns (rows 1–3, columns 10–11).
Orange occupies 4 squares within rows 9–11, columns 1–2.
Slate: 8 squares across rows 1–5, columns 10–12.
Pale yellow covers 10 squares, spanning 4 rows and 4 columns (rows 6–9, columns 9–12).
Red occupies 14 squares within rows 3–6, columns 4–10.
Sea green: 14 squares across rows 6–12, columns 1–4.
Amber covers 15 squares, spanning 3 rows and 7 columns (rows 1–3, columns 3–9).
Mint occupies 18 squares within rows 1–5, columns 1–5.
Khaki: 22 squares across rows 5–11, columns 3–8.
Teal covers 30 squares, spanning 5 rows and 9 columns (rows 8–12, columns 4–12).
Where to start on this board
Blue is the natural opening on #26: it is the smallest region on the grid at 2 squares, boxed into rows 2–3 and columns 11–11. Since one of those squares must hold a queen, that block of 2 rows and 1 column is the most contested part of the board.
Because blue stays inside column 11, its queen belongs to that column and no other region may use it. Cross out the rest of column 11 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. Rose 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 #26
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 4, 7 and 12 are the narrowest, touched by only 3 colors. Column 12 is the tightest column, with 3 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 11 rows. By contrast row 3 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
With twelve queens to seat and twelve regions competing over 144 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 12x12 boards quickly and players who stall halfway.
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 #26 is rated hard
The rating reflects how much the board concedes up front. Puzzle #26 has one region confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 28 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
If #26 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 12x12
At 12x12 you are managing 144 squares, and holding the whole board in your head will not work. Split it into quadrants and solve locally. Most useful deductions on a grid this large are regional — a color pinched between two placed queens, or a band of rows that two regions must share. Trust the marks on the board over your memory.
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 #26, start hunting for it near row 4.
As a sanity check rather than a spoiler: the finished solution to #26 puts 4 queens on the outer border and 8 queens in the interior, with none in a 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 12x12 Queens puzzle #26?
Puzzle #26 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #26 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #26, has been verified to have exactly one valid arrangement of twelve queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #26?
Start with the blue region — the most constrained color on this board, with 2 squares spanning rows 2–3 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.