8x8 Queens Puzzle #228
Difficulty: easy. Place 8 queens on this 8x8 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 15-step reasoning is written out below.
Previous puzzle · All 8x8 puzzles · Next puzzle
Step-by-step solution for puzzle #228
What follows is a complete solve of puzzle #228, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 8 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 confined to one line, region shadow, pairing argument on rows, last square in a region.
Show the full walkthrough (8 steps) — contains the solution
Step 1. Amber cannot leave column 8 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 8 squares in all.
Step 2. Indigo is down to 3 candidates in rows 1 and 2, columns 5 and 6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
Step 3. The khaki region has 3 squares left, spread across rows 7 and 8, columns 4 and 5. 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 5 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 8 queens placed. Step 5. Indigo and amber are now boxed into rows 1 and 2 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 8 squares at once.
Step 6. Here is the pairing argument. The pale yellow and khaki regions have no open squares outside rows 7 and 8 — 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: 4 squares come off in one stroke.
Step 7. Red cannot leave column 6 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 7 squares in all.
Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: indigo has one square left, so its queen takes row 1, column 5; amber has one square left, so its queen takes row 2, column 8; mint has one square left, so its queen takes row 4, column 7; red has one square left, so its queen takes row 6, column 6; khaki has one square left, so its queen takes row 8, column 4; slate has one square left, so its queen takes row 5, column 2; pale yellow has one square left, so its queen takes row 7, column 1; blue has one square left, so its queen takes row 3, column 3. 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 3, column 3.
The board after step 8 — 8 of 8 queens placed.
That completes the board: 8 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 8x8 Queens puzzle #228
This is puzzle number 228 in the 8x8 collection, rated easy. The grid holds 64 squares split between eight colored regions, and a finished board carries eight 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 #228, 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 eight regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #228 are: amber (2 squares), khaki (3 squares), indigo (4 squares), pale yellow (5 squares), red (9 squares), slate (10 squares), mint (11 squares), blue (20 squares). An even split would hand every color 8 squares, so the amber region is running 6 squares under that average while the blue region is the roomiest area on the grid with 20 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Amber is working with 2 squares while blue has 20 to spare, a gap of 18. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The amber region is the most compact color here, filling 100% of the 2×1 box that encloses it, while mint is the most scattered at 55% 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
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.
Amber: 2 squares across rows 1–2, columns 8–8. It sits wholly inside column 8, so its queen must be in that column.
Khaki covers 3 squares, spanning 2 rows and 2 columns (rows 7–8, columns 4–5).
Indigo occupies 4 squares within rows 1–2, columns 5–7.
Pale yellow: 5 squares across rows 7–8, columns 1–3.
Red covers 9 squares, spanning 4 rows and 3 columns (rows 5–8, columns 6–8).
Slate occupies 10 squares within rows 5–7, columns 1–5.
Mint: 11 squares across rows 2–6, columns 5–8.
Blue covers 20 squares, spanning 5 rows and 5 columns (rows 1–5, columns 1–5).
Where to start on this board
The most constrained color is where a solve should begin, and on #228 that is amber with 2 squares. It reaches from row 1 to row 2 and from column 8 to column 8 — 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 amber stays inside column 8, its queen belongs to that column and no other region may use it. Cross out the rest of column 8 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. Indigo, pale yellow and khaki 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 #228
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3 and 4 are the narrowest, touched by only 2 colors. Columns 1, 2, 3, 4, 6, 7 and 8 are the tightest columns, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 7 rows. By contrast row 7 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
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.
The whole middle game reduces to two sweeps. Sweep the eight colors looking for one with a single square left; sweep the eight rows and eight columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 8x8 solve from a stalled one.
Resist the plausible-looking queen. On #228 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 #228 is rated easy
The easy label comes out of four measurable things about #228: one of its regions is locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 2 colors, and its largest and smallest regions differ by 18. 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.
Stuck on #228 despite the easy 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 8x8
At 8x8 the whole grid stays within a single glance, which makes systematic scanning practical. Read the rows in order and count the colors in each — a row touched by two colors is far more constrained than one touched by five, and that is usually where the next forced move hides. The board is small enough that re-scanning from the top after each placement costs almost nothing.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 3 on this board.
As a sanity check rather than a spoiler: the finished solution to #228 puts 4 queens on the outer border and 4 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 8x8 Queens puzzle #228?
Puzzle #228 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 8x8 puzzle #228 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #228, has been verified to have exactly one valid arrangement of eight queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #228?
Start with the amber region — the most constrained color on this board, with 2 squares spanning rows 1–2 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.