# Can you provide a hint on how to solve this Hex Cube puzzle?

I've been tackling this puzzle named "Hex Cube" which comes with the instructions "Can you decipher the message? You should be able to if you go back to basics and use a little bit of logic.":

Reproduced here in black and white:

         22 5b 61
50 76 6d
77 2a 63
2a 6d 74 70 7c 72 76 76 3f
48 6d 6f 34 77 7a 6a 78 7e
7c 7a 3a 78 78 7e 3f 6a 3a
77 61 2b
75 77 58
6a 76 79
6a 50 66
3f 75 68
6b 75 73


There are 30 different hexadecimal symbols in this 54-symbol message, all in the printable character range of 7-bit ASCII (0x22-0x7f):

      " [ a
P v m
w * c
* m t p | r v v ?
H m o 4 w z j x ~
| z : x x ~ ? j :
w a +
u w X
j v y
j P f
? u h
k u s


In response to @JimN's comment, here is the binary representation:

                           00100010 01011011 01100001
01010000 01110110 01101101
01110111 00101010 01100011

00101010 01101101 01110100 01110000 01111100 01110010 01110110 01110110 00111111
01001000 01101101 01101111 00110100 01110111 01111010 01101010 01111000 01111110
01111100 01111010 00111010 01111000 01111000 01111110 00111111 01101010 00111010

01110111 01100001 00101011
01110101 01110111 01011000
01101010 01110110 01111001

01101010 01010000 01100110
00111111 01110101 01101000
01101011 01110101 01110011


This is a Rubik's Cube which can be solved using an online tool in 20 rotations:

R2 U F' U B2 R F' U' D2 R' U L2 U2 D' B2 R2 U' R2 F2 R2

Solved cube:

Shown here in black and white:

         6a 50 63
7a 76 50
22 6a 79
7c 6a 6b 2a 58 66 7a 76 72
76 6d 34 6f 77 2a 7c 78 7a
70 75 6f 2b 68 61 73 48 3a
7e 7e 3f
5b 77 3f
74 61 77
77 78 78
6d 75 75
6a 6d 76


And the corresponding ASCII characters are:

      j P c
z v P
" j y
| j k * X f z v r
v m 4 o w * | x z
p u o + h a s H :
~ ~ ?
[ w ?
t a w
w x x
m u u
j m v


And the binary representation:

                           01101010 01010000 01100011
01111010 01110110 01010000
00100010 01101010 01111001

01111100 01101010 01101011 00101010 01011000 01100110 01111010 01110110 01110010
01110110 01101101 00110100 01101111 01110111 00101010 01111100 01111000 01111010
01110000 01110101 01101111 00101011 01101000 01100001 01110011 01001000 00111010

01111110 01111110 00111111
01011011 01110111 00111111
01110100 01100001 01110111

01110111 01111000 01111000
01101101 01110101 01110101
01101010 01101101 01110110


I figure "back to basics" could refer to "transposition and substitution". Solving the cube would be the transposition part. For the substitution part, I'm thinking "a bit of logic" could mean some bitwise operation.

That's where I'm stuck. I've tried a number of things (e.g. frequency analysis, ASCII shift) to no avail and could use a hint, if anyone has an idea on how to solve this!

2021-04-18 UPDATE: I wonder if there could be a relation between the rotation of the cubelets from the initial to the solved position and some "bit of logic" (bitwise) operations. The cubelet rotations of the solved cube are show below, where: 0: no rotation; 1: 90° rotation; -1: -90° rotation; and 2: 180° rotation.

          0  1 -1
2  0  1
-1  0  0

1 -1  2  0 -1  0   2  2  0
-1  0  2  2  0 -1  -1  0 -1
-1  0 -1  2  1 -1   1 -1  0

2 -1  0
-1  0  2
2  2  2

1  2  2
2  0  2
0  2  2

• Can you show the printable ASCII characters of the given table (before applying the rubik's solution?)
– JimN
Sep 7 '20 at 7:35
• @JimN, good idea; I edited the post to add that, along with my thoughts on the "back to basics" and "a bit of logic" phrases from the instructions. Sep 7 '20 at 14:27
• "Back to basics" could simply be a play on the word "base" as in having to interpret the numbers in base16. Could you also covert the before and before hex symbols into base-2 (binary) and see if a picture emerges in the 0s and 1s ?
– JimN
Sep 7 '20 at 22:50
• Maybe trying to change binary back to numbers, maybe that is what back to basics means @fstarnaud Jan 28 at 6:36
• "hasH" is very conspicuously present in the solved cube... Apr 4 at 1:32