The number of possible surface combinations - allowing that a
space could have any of the four pieces showing at any level or be
blank is 17 to the 33rd power or 
40,252,497,110,927,943,179,349,807,054,456,171,205,137. 
If someone attempted to put together this puzzle in every possible
combination and completed one solution every tenth of a second, 
it would take longer than the predicted life span of the universe.