Rubik's Solver

Puzzle diagnosis · checked 22 September 2026

Nine of each colour. Still no solution?

A 3×3 colouring can pass the count check and still describe a position that face turns cannot reach. This guide uses three deliberately invalid positions from our own piece model to show the difference between counting stickers and checking a puzzle.

Check the description before blaming the toy

The solver sees painted stickers, not the physical mechanism. An impossible entry usually deserves another look at the hidden faces before you conclude that the toy needs repair. A back face copied as a mirror image can describe different pieces from the ones you are holding.

  1. Read the six centres. On a standard 3×3, those define the colour scheme. Keep the same upper and front faces as references. You do not need to assume that white is on top.
  2. Check counts. Each of the six colours must occur nine times. A duplicate centre or a missing sticker must be corrected before a piece-level diagnosis is useful.
  3. Read each edge as a pair. Its two stickers belong to one piece. Do the same for the three stickers on every corner, preserving their order around that corner.
  4. Compare the starting screen with the toy. A legal solution to a different entry can be perfectly correct and still fail on your physical cube.

Do not dismantle a puzzle because a single entry was rejected. If you cannot locate a copying error, save clear views of all six faces and send a reproducible report.

Three positions that counting alone cannot detect

Each diagram starts from our default solved colour scheme and changes only the named piece or pieces. Every example still has nine stickers of each colour. The quoted error is the actual result returned by this site's 3×3 parser for that illustrated position. These are teaching counterexamples, not legal scrambles to perform on your toy.

Faces are viewed from outside. W white · Y yellow · G green · B blue · R red · O orange. The letters describe colours; the face names above the maps describe positions.

1. One flipped edge

The two stickers on one edge exchange places. There are still nine stickers of every colour, but normal face turns cannot produce a single edge flip.

One flipped edge Up: white W Up: white W Up: white W Up: white W Up: green G Up: white W Up: white W Up: white W Up: white W Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Right: red R Right: red R Right: red R Right: red R Right: red R Right: red R Right: red R Right: red R Right: red R Left: orange O Left: orange O Left: orange O Left: orange O Left: orange O Left: orange O Left: orange O Left: orange O Left: orange O Front: green G Front: green G Front: green G Front: green G Front: white W Front: green G Front: green G Front: green G Front: green G Back: blue B Back: blue B Back: blue B Back: blue B Back: blue B Back: blue B Back: blue B Back: blue B Back: blue B UpDownRightLeftFrontBack
One flipped edge: correct counts, unreachable by legal face turns.

This colouring is impossible — an edge is flipped, which cannot happen without taking the cube apart. Re-check the edge stickers.

2. One twisted corner

Three stickers cycle around one corner. Its three colours and every colour total are unchanged, but the total corner twist is no longer valid.

One twisted corner Up: green G Up: white W Up: white W Up: white W Up: white W Up: white W Up: white W Up: white W Up: white W Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Right: white W Right: red R Right: red R Right: red R Right: red R Right: red R Right: red R Right: red R Right: red R Left: orange O Left: orange O Left: orange O Left: orange O Left: orange O Left: orange O Left: orange O Left: orange O Left: orange O Front: red R Front: green G Front: green G Front: green G Front: green G Front: green G Front: green G Front: green G Front: green G Back: blue B Back: blue B Back: blue B Back: blue B Back: blue B Back: blue B Back: blue B Back: blue B Back: blue B UpDownRightLeftFrontBack
One twisted corner: correct counts, unreachable by legal face turns.

This colouring is impossible — a corner is twisted, which cannot happen without taking the cube apart. Re-check the colours around each corner.

3. Only two edges swapped

Two edge pieces exchange places while every corner stays put. Even without a flipped edge, this disagrees with the permutation parity of the corners.

Only two edges swapped Up: white W Up: white W Up: white W Up: white W Up: red R Up: green G Up: white W Up: white W Up: white W Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Right: red R Right: red R Right: red R Right: red R Right: white W Right: red R Right: red R Right: red R Right: red R Left: orange O Left: orange O Left: orange O Left: orange O Left: orange O Left: orange O Left: orange O Left: orange O Left: orange O Front: green G Front: green G Front: green G Front: green G Front: white W Front: green G Front: green G Front: green G Front: green G Back: blue B Back: blue B Back: blue B Back: blue B Back: blue B Back: blue B Back: blue B Back: blue B Back: blue B UpDownRightLeftFrontBack
Only two edges swapped: correct counts, unreachable by legal face turns.

This colouring is impossible — two pieces are swapped, which cannot happen without taking the cube apart. Re-check your stickers.

These constraints are different checks. Fixing an edge flip does not automatically fix a corner twist or an isolated piece swap. A validator may report the first detectable problem, so correcting one entry mistake can reveal another.

What the error does, and does not, tell you

A rejection establishes a problem with the entered position under this puzzle's rules. It cannot establish whether a sticker was mistyped, a corner was twisted by hand, the cube was reassembled incorrectly, or a validator has a bug. That distinction requires checking the physical puzzle and the exact input.

If the toy was taken apart or re-stickered, mention that history in a support report. Follow the manufacturer's instructions for physical repair. Never force a corner or an edge because a web page tells you that the colour pattern is invalid.

If the position is accepted but the physical solve goes wrong, stop at the first mismatch. Undo your last physical turn and move Back on screen. Check the named face, direction and grip. Asking for another solution without correcting a mismatched starting position does not repair that mismatch.

For a known legal comparison, use the four-turn 3×3 worked example. It gives an exact setup from solved, diagrams after every undo step, and a button that loads the same position into the solver. A random Scramble is useful for on-screen practice, but it does not scramble the cube in your hands.

Do not apply the 3×3 rules to every puzzle

A 2×2 has only corners and no fixed centre stickers. Its reference corner determines the final scheme. A Skewb has centres, but they move during legal corner turns. Assuming that either puzzle behaves like a 3×3 produces misleading checks.

A Pyraminx has independent tips. A lone tip twist is legal and needs a tip move; it is not the same as an impossible twisted corner on a cube. A Pyramorphix changes shape and has a different mechanism despite its similar outline. Count the stickers and identify the mechanism before choosing a solver.

How to check this explanation

The diagrams are generated from this project's piece geometry, and all three illustrated colourings are passed through the same parser as the interactive solver. Tests check their colour counts and their rejection. The worked examples on the solver pages provide legal positions whose setup and inverse are replayed and checked independently.

For the mathematics behind 3×3 edge orientation, corner orientation and permutation parity, see Herbert Kociemba's cubie-level description. For our search methods and their limits, see how this site verifies solutions.