IBM Ponder This #184 · August 2013

Put five-bit numbers on the vertices of a 9-dimensional hypercube such that, from any vertex, you can reach any number in no more than two moves along the edges of the hypercube.
Please provide the answer as a string of 512 characters using the following alphabet: ABCDEFGHIJKLMNOPQRSTUVWXYZ012345.
To clarify, here is a solution for the same problem with four-bit numbers on a 5-dimensional hypercube, where you can get to any number from any vertex by at most two moves along the edges:
"KLICHBEFMJAGPONDDNOPGAJMFEBHCILK"
This refers to:
Vertex Character(Value)
---------   ----------------
00000   K(10)
00001   L(11)
00010   I(8)
00011   C(2)
00100   H(7)
00101   B(1)
00110   E(4)
00111   F(5)
01000   M(12)
01001   J(9)
01010   A(0)
01011   G(6)
01100   P(15)
01101   O(14)
01110   N(13)
01111   D(3)
10000   D(3)
10001   N(13)
10010   O(14)
10011   P(15)
10100   G(6)
10101   A(0)
10110   J(9)
10111   M(12)
11000   F(5)
11001   E(4)
11010   B(1)
11011   H(7)
11100   C(2)
11101   I(8)
11110   L(11)
11111   K(10)

Each vertex of the five-dimensional hypercube is represented by five bits; this example uses only the first half of the alphabet: from A(0) to P(15).
Please wait for September with August's solution.

Solution

Best opened after a real attempt

To be added.