• On each face of each cube one of the digits from 0 to 8 is written, with each of those digits appearing on more than one of the cubes.
• The sum of the digits on each cube is the same.
• By moving the cubes around Georgia can make the top faces form many numbers (with the 6 being also used for a 9); including all the three digit perfect squares.
Determine the total number of three-digit perfect cubes that Georgia cannot construct in this way.
Note: Adapted from an Enigma Puzzle which appeared in 'New Scientist' in 1994.
