Assume a base cuboid of 20 dimensions contains only two base cells: (1) (a1,a2,b

Question

Assume a base cuboid of 20 dimensions contains only two base cells: (1) (a1,a2,b3,b4,...,b19,b20), and (2) (b1,b2,b3,b4,...b19,b20), where ai not equal bi (for any i). The measure of the cube is count.
1) How many nonempty aggregated (i.e., non-base) cells a complete cube will contain?                                             >
2) How many nonempty aggregated cells an iceberg cube will contain, if the condition of the iceberg cube is "count _ 2"?
3) How many closed cells in the full cube? Note that a cell is closed if none of its descendant cells has the same measure (i.e., count) value. For example, for a 3-dimensional cube, with two cells: "a1a2a3 : 3" , "a1*a3 : 3   , the first is closed but the second is not.

Explanation / Answer

1) 2^20 2)Each base cell generates 2^(20?1) non-base cells, so there are 2*(3*(20?1) non-base cells before aggregating the measure. 3) 4 close cells 2 base cells + 2 cells that overlap once

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