I just peel the stickers off!

Statement

Goal

Can a Rubik's cube be solved by Restickering™?

A popular method to pretend you can solve the Rubik's cube when no one's watching is to peel the stickers off and glue them back into place. It's not a very good method, as it tends to damage the stickers irreparably, but from a theoretical point of view it does the job.

Feliks has left his scrambled cube on the table for only a few minutes, but as he comes back from his break, he notices an evil grin on Lucas's face. Has Lucas been messing around with the cube and spare stickers in a way that makes it unsolvable using the Restickering™ method? Help Feliks by telling him whether or not he can peel and glue the stickers back into place.

You are given a cube state in pattern format. A solved cube looks like this:


    UUU
    UUU
    UUU

LLL FFF RRR BBB
LLL FFF RRR BBB
LLL FFF RRR BBB

    DDD
    DDD
    DDD

Letters ULFRBD mean “this sticker belongs on the Up/‌Left/‌Front/‌Right/‌Back/‌Down face”.

A monochrome cube, e.g. with only U stickers, is obviously unsolvable using the Restickering™ method.

A cube where an R′ move (right face counterclockwise quarter turn, in standard notation) has been applied is solvable using the Restickering™ method and looks like the example below.

Input

11 lines (including 2 blank): a cube pattern

Output

SOLVABLE if it is possible to peel the stickers off and glue them back in a solved cube.
UNSOLVABLE otherwise.

Constraints

Apart from the stickering, all cubes are standard 3×3×3 Rubik's cubes.
Only valid sticker colors are provided.

Example

Input

    UUB
    UUB
    UUB

LLL FFU RRR DBB
LLL FFU RRR DBB
LLL FFU RRR DBB

    DDF
    DDF
    DDF

Output

SOLVABLE

Game modes

Fastest, Shortest, Reverse

Test cases

R′ Test

Input

UUB UUB UUB LLL FFU RRR DBB LLL FFU RRR DBB LLL FFU RRR DBB DDF DDF DDF

Output

SOLVABLE

L Validator

Input

BUU BUU BUU LLL UFF RRR BBD LLL UFF RRR BBD LLL UFF RRR BBD FDD FDD FDD

Output

SOLVABLE

Solved Test

Input

UUU UUU UUU LLL FFF RRR BBB LLL FFF RRR BBB LLL FFF RRR BBB DDD DDD DDD

Output

SOLVABLE

x2 Validator

Input

DDD DDD DDD LLL BBB RRR FFF LLL BBB RRR FFF LLL BBB RRR FFF UUU UUU UUU

Output

SOLVABLE

Pure White Test

Input

UUU UUU UUU UUU UUU UUU UUU UUU UUU UUU UUU UUU UUU UUU UUU UUU UUU UUU

Output

UNSOLVABLE

Pure Yellow Validator

Input

DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD

Output

UNSOLVABLE

L2 D R′ D′ F′ D′ R D′ R2 F2 Test

Input

DUD DUU BDL LLL UFF ULR FBF LLR BFF URB DBF FRD BUU BFB DBR LRR DDR ULR

Output

SOLVABLE

M2 E2 S2 Validator

Input

UDU DUD UDU LRL FBF RLR BFB RLR BFB LRL FBF LRL FBF RLR BFB DUD UDU DUD

Output

SOLVABLE

UF edge flip Test

Input

UUU UUU UFU LLL FUF RRR BBB LLL FFF RRR BBB LLL FFF RRR BBB DDD DDD DDD

Output

SOLVABLE

UF edge flip on L2 D R′ D′ F′ D′ R D′ R2 F2 Validator

Input

DUD DUU BFL LLL UDF ULR FBF LLR BFF URB DBF FRD BUU BFB DBR LRR DDR ULR

Output

SOLVABLE

UFR corner twist Test

Input

UUU UUU UUF LLL FFR URR BBB LLL FFF RRR BBB LLL FFF RRR BBB DDD DDD DDD

Output

SOLVABLE

UFR corner twist on L2 D R′ D′ F′ D′ R D′ R2 F2 Validator

Input

DUD DUU BDF LLL UFU LLR FBF LLR BFF URB DBF FRD BUU BFB DBR LRR DDR ULR

Output

SOLVABLE

Random stickers Test

Input

LRD DFR RBD ULF LRB DBD LLB RLL BUU BFD FFU BDR URL UDF RFL FBU LRU DFU

Output

UNSOLVABLE

Other random stickers Validator

Input

UFD URL UBF LFR FDU LRU RDB UFF DFB UUB LLR BLL DBD BRL FLU DBR RFD DRL

Output

UNSOLVABLE

More random stickers Test

Input

BDL DBL LUR BFR BBD LUFDUR UBR RRD DLDFUR RBF FUU FRFBFD UBF LLD LUR

Output

UNSOLVABLE

More other random stickers Validator

Input

UUR RBL FDB LLU DBD URD LFU UFR FDB ULB DBR FFL RLF BLB BLD LUF FRD URR

Output

UNSOLVABLE

Solution language

Solution

Stub generator input

Comments

7 Comments

damaltor Unnamed CodinGamer

about 9 years ago

I think that this maybe even is a bit too trivial... but for a clash it could be working because you might even be able to one-line it in some languages :D

JBM Unnamed CodinGamer

My forecast is that it's going to be *very* dependent on who reads it. Some are going to panic at the very sight of "Rubik", others are going to recognize it for the trivial problem it is. The more general point is: it's the easiest in the series, but it has its place. It's doable in clash (hence my submitting it there), but it could actually make sense to duplicate it to community puzzles once the others "can it be solved this way" are approved, to enable a more gradual difficulty slope. My proposed sample solution is 78 characters (though I'll admit I didn't spend as much on it as I would have on a clash). How long is yours? :D

Submitting as clash because the solution's really trivial, but I really have no problem whatsoever with it moving to Puzzles if it's deemed to complex a statement for clashing. (Sorry, no clashing in a long time on my side, I might be out of touch) Please be careful if you edit: I've put a few ZERO WIDTH NON-JOINERs around to help general appearance.

nicola Unnamed CodinGamer

I edited the "x2" case, the first empty line was wrong.