12x12 Queens Puzzle #148
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 24-step reasoning is written out below.
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Step-by-step solution for puzzle #148
What follows is a complete solve of puzzle #148, worked the way a person works it rather than the way a computer does. It runs to 24 deductions — 12 queen placements and 12 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 confined to one line, region shadow, pairing argument on columns, last square in a region, pairing argument on rows, line confined to one region, last square in a column, last square in a row.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Orange cannot leave row 9 — every one of its open squares (2 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 14 squares in all.
Step 2. Sea green is down to 5 candidates in rows 10–12, columns 10–12, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about sea green itself.
Step 3. The rose region has 3 squares left, spread across rows 11 and 12, columns 9 and 10. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
Step 4. Here is the pairing argument. The red, orange, sea green, and rose regions have no open squares outside columns 9–12 — 4 colours confined to 4 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 18 squares come off in one stroke.
Step 5. Only row 1, column 8 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 8, the rest of the indigo region and every square adjacent to it — diagonals included.
The board after step 5 — 1 of 12 queens placed. Step 6. The amber region has 3 squares left, spread across rows 2–4, columns 6 and 7. 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 7. Wherever teal 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. Here is the pairing argument. The teal and rose regions have no open squares outside rows 11 and 12 — 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: 13 squares come off in one stroke.
Step 9. 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: sea green has one square left, so its queen takes row 10, column 10; orange has one square left, so its queen takes row 9, column 12; rose has one square left, so its queen takes row 12, column 9; teal has one square left, so its queen takes row 11, column 7; 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.
Step 10. Blue is down to 3 candidates in rows 3 and 4, columns 2 and 3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about blue itself.
The board after step 10 — 6 of 12 queens placed. Step 11. The khaki region has 3 squares left, spread across rows 7 and 8, columns 1 and 2. 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 12. Wherever slate ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 13. Column 5 has only pale yellow squares left (5 open squares). The column needs a queen and only pale yellow can provide one, which pins that colour to this column and kills its squares elsewhere: 4 squares.
Step 14. Every open square left in column 4 (3 open squares) belongs to the slate region. Since that column must contain a queen, slate is the colour that supplies it — so slate squares anywhere else on the board are out, 3 squares in all.
Step 15. 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: column 3 is down to one square, putting a queen on row 3, column 3; slate has one square left, so its queen takes row 5, column 4; row 4 is down to one square, putting a queen on row 4, column 1; khaki has one square left, so its queen takes row 8, column 2; pale yellow has one square left, so its queen takes row 7, column 5; red has one square left, so its queen takes row 6, column 11. 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 6, column 11.
The board after step 15 — 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 #148
This is puzzle number 148 in the 12x12 collection, rated hard. The grid holds 144 squares split between twelve colored regions, and a finished board carries twelve queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
There is exactly one way to finish #148, 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 twelve regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #148 are: orange (2 squares), rose (4 squares), mint (7 squares), slate (8 squares), sea green (8 squares), blue (10 squares), khaki (12 squares), indigo (13 squares), red (14 squares), teal (14 squares), amber (17 squares), pale yellow (35 squares). An even split would hand every color 12 squares, so the orange region is running 10 squares under that average while the pale yellow region is the roomiest area on the grid with 35 squares.
Every color takes one queen and one only, whatever its size — which is why the 33 square difference between orange and pale yellow 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.
Shape matters as much as size. The orange region is the most compact color here, filling 100% of the 1×2 box that encloses it, while amber is the most scattered at 40% of its 6×7 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
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.
Orange covers 2 squares, spanning 1 row and 2 columns (rows 9–9, columns 11–12). It never leaves row 9, so its queen is locked to that row.
Rose occupies 4 squares within rows 11–12, columns 9–11.
Mint: 7 squares across rows 1–6, columns 1–2.
Slate covers 8 squares, spanning 5 rows and 3 columns (rows 3–7, columns 2–4).
Sea green occupies 8 squares within rows 9–12, columns 10–12.
Blue: 10 squares across rows 1–4, columns 2–5.
Khaki covers 12 squares, spanning 6 rows and 3 columns (rows 7–12, columns 1–3).
Indigo occupies 13 squares within rows 1–3, columns 8–12.
Red: 14 squares across rows 4–8, columns 9–12.
Teal covers 14 squares, spanning 6 rows and 4 columns (rows 7–12, columns 6–9).
Amber occupies 17 squares within rows 1–6, columns 5–11.
Pale yellow: 35 squares across rows 3–12, columns 2–7.
Where to start on this board
The most constrained color is where a solve should begin, and on #148 that is orange with 2 squares. It reaches from row 9 to row 9 and from column 11 to column 12 — 1 row by 2 columns. 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 orange never leaves row 9, its queen must be in that row — and that instantly settles row 9 for everyone else. Sweep along it and X out every square that is not orange. 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. 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 #148
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 8 and 10 are the narrowest, touched by only 4 colors. Column 1 is the tightest column, with 2 colors.
A line with few colors is a line close to resolving. Where only 4 colors appear, one of them owns the row outright and the others must fit into the remaining 11 rows. Row 4 is the crowded extreme at 6 colors — worth revisiting later, not now.
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.
Two checks, run alternately, will carry you through the 144 squares of this grid. First: has any of the twelve regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 12x12 boards almost always run one of those checks and forget the other.
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 #148 is rated hard
Ratings track how generous the opening is. On #148 you get one region pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 4 colors, and a 33-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
Stuck on #148 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 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.
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 #148 is column 1.
A non-spoiling distribution check: solved, #148 carries 4 queens on the perimeter against 8 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 12x12 Queens puzzle #148?
Puzzle #148 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 4 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #148 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #148, 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 #148?
Start with the orange region — the most constrained color on this board, with 2 squares spanning rows 9–9 and columns 11–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.