New Scientist Enigma 967 – Prime Cubes
by Colin Singleton
From New Scientist #2122, 21st February 1998
George has 27 small blocks which have been identified with 27 different prime numbers — each block has its number on each face. He has assembled the blocks into a 3 x 3 x 3 cube,. On each of the three visible faces, the nine numbers total 320 — but this is not true of the three hidden faces.
George remembers that when he bought the blocks they were assembled into a similar 3×3×3 cube, but on that occasion they showed the same total on each of the six faces, this being the smallest possible total if each block has a different prime number.
What was the total on each face when George bought the blocks?