(New Dice) The answer to the question is 'yes'. This problem was published by Martin Gardner in his Scientific American column "Mathematical Games". The solution to this problem is due to George Sicherman (and the dice are sometimes called Sicherman dice).
The renumbering of the dice is as follows :
1, 3, 4, 5, 6, 8 and 1, 2, 2, 3, 3, 4.
Please also see the following journal articles :
Gallian, J. A.; Rusin, D. J. (1979), "Cyclotomic polynomials and nonstandard dice", Discrete Mathematics 27 (3): 245–259
Broline, D. (1979), "Renumbering of the faces of dice", Mathematics Magazine (Mathematics Magazine, Vol. 52, No. 5) 52 (5): 312–315
(Chandrayaan Engine Room) The answer to this puzzle is straight forward but it takes some thinking to get to. The solution is the following : Shut off the neutrino drive. Then, take the two wires A and B. Light wire A on both ends and simultaneously light wire B at one end. Wire A will take exactly half an hour to burn. At this point, 30 minutes worth of Wire B has been burned. So, now light Wire B at the other end. This will take exactly 15 minutes. When Wire B burns out, start the positron motor.