2x2x3Loading…

2x2x3 simulator and solver

Play a virtual 2x2x3 in your browser, or enter the colors of your own 2x2x3 and get a solution. Also known as Tower Cube.

Info

Pieces
TypeCountStickersPositionsOrientation (physical)Orientation (visual)
242422
383811
One row per orbit. Orientation counts are per position; multiple values mean positions differ.
Stickers
32
Axes
34 cut planes across them
Solver
Available
Distinct-piece states
≈ 241,9201,935,360 arrangements of the stickers the moves reach (Schreier–Sims)÷ 8 turns of the whole puzzle= 241,920Tracks individual sticker identities, even on identical-looking pieces; whole-puzzle rotations are identified. Invisible rotations of a piece and internal pieces are not counted.
Visually distinct states
Not computedVisually distinct states = distinct-piece states ÷ reachable indistinguishable arrangements.Reachable indistinguishable arrangements = 1 × reachable fraction.No visually interchangeable sticker-bearing pieces were found.The reachable fraction accounts for restrictions such as permutation parity. Computing the correct fraction and the final visual state count is not yet implemented.
Put together at random
1 in 8 reaches the original sticker identities8!·1⁸ · 4!·2⁴ = 15,482,880 ways to put the pieces in: per type of piece, its pieces in any order and each in any orientation that looks different÷ 1,935,360 arrangements the moves reach = 8This uses distinct piece identities; the chance of reaching a visually solved state may be higher.

Moves

Face turns

x
y
z

2×2×3 beginner method

Solve the two square end layers, then align and permute the four middle pieces.

Keep the long axis vertical. U and D are quarter-turns; R, L, F, and B each mean one 180° side turn. E turns the middle layer. Whole-puzzle setups are explicit.

Top-face colors

Bring the four top-color corners onto the square upper face.

  1. Hold the long axis vertically, with square faces above and below.
  2. Build three matching top stickers using simple turns, then insert the fourth corner.
  3. Side colors will be matched in the next phase.

Insert the fourth top-face corner

R D R

Put the replacement corner below its working slot, insert it, and restore the other top-color corners.

Top-layer corner positions

Match the side stickers of the four upper corners.

  1. Align the upper layer with the reference frame.
  2. Use an adjacent or diagonal swap for the corners that remain in the wrong positions.

Before this phase: Top-face colors.

Top corners — adjacent swap

(F U' F U F) (R U R U' R) U

Swap the indicated top corners, including the final layer alignment. The bottom corners are preserved.

Top corners — diagonal swap

R U2 F U R U2 F U' R U2 F U'

Swap the indicated top corners, including the final layer alignment. The bottom corners are preserved.

Bottom-layer corner positions

Solve the lower corners while preserving the upper layer.

  1. The opposite end face already has the correct color because the first end's corners are together.
  2. Prepare the turned-over hold and use the same corner swaps. A later preparation supplies any necessary regrip.

Before this phase: Top-face colors, Top-layer corner positions.

Bottom corners — adjacent swap

[x: (F U' F U F) (R U R U' R) U]

Prepare the turned-over hold, then swap the bottom corners. The previously completed corners stay solved.

Bottom corners — diagonal swap

[x: R U2 F U R U2 F U' R U2 F U']

Prepare the turned-over hold, then swap the bottom corners. The previously completed corners stay solved.

Middle layer

Align, swap, or cycle the four middle pieces to finish the Tower Cube.

  1. First rotate E to match as many middle pieces as possible.
  2. If none can match, use the reference-match sequence and its final regrip.
  3. Swap adjacent or diagonal pieces, or cycle the last three. Both end layers remain solved.

Before this phase: Top-face colors, Top-layer corner positions, Bottom-layer corner positions.

Make a middle-layer reference match

(R U2 D2 L) y2

Use this when the middle pieces cannot align with the solved ends. The final half-turn regrip restores the corners to the reference hold.

Middle — adjacent swap

(R U2)3

Swap or cycle middle pieces while keeping both end layers solved.

Middle — three-cycle

R U D' F U' D

Swap or cycle middle pieces while keeping both end layers solved.

Well known algorithms and patterns

Beginner — Tower Cube

Insert fourth top-face corner

R D R

Square faces on top/bottom. Top wrong-color corner at front right, bottom replacement at front left. Side-face letters are half turns.

Top corners — adjacent swap

(F U' F U F) (R U R U' R) U

Swap UFR and UFL; solve the top face first. Includes the final U alignment needed to finish the named swap. Turn the puzzle over to use this for the bottom layer. Published expression: F U' F U F R U R U' R

Top corners — diagonal swap

R U2 F U R U2 F U' R U2 F U'

Swap UFR and UBL; solve the top face first. Includes the final U' alignment needed to finish the named swap. Published expression: R U2 F U R U2 F U' R U2 F

Middle — make a reference match

R U2 D2 L

Use only when no middle-layer piece can match the aligned top and bottom layers.

Middle — adjacent swap

(R U2)3

Keep the two middle pieces to swap on the right-hand side.

Middle — diagonal swap

[F: (R U2)3]

Swap the front-left and back-right middle pieces.

Middle — three-cycle

R U D' F U' D

Keep the correct middle piece at back left. Repeat once if the cycle is in the other direction.