O'Halloran numbers: Difference between revisions

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For this task, a cuboid is a regular 3-dimensional rectangular object, with six faces, where all angles are right angles, where opposite faces of the cuboid are equal, and where each dimension is a positive integer unit length.
For this task, the term "cuboid" means a 3-dimensional object with six rectangular faces, where all angles are right angles, where opposite faces are equal, and where each dimension is a positive integer unit length.


The surface area of a cuboid so-defined is two times the length times the width, plus two times the length times the height, plus two times the width times the height. A cuboid will always have an even integer surface area. The minimum surface area a cuboid may have is 6; one where the '''l''', '''w''', and '''h''' measurements are all 1:
The surface area of a cuboid so-defined is two times the length times the width, plus two times the length times the height, plus two times the width times the height. For example, a cuboid with l = 2, w = 1 h = 1 has a surface area of 10:

⚫
2 × ( l × w + w × h + h × l )
⚫
2 × ( 1 × 1 + 1 × 1 + 1 × 1 ) = 6

Notice that the total surface area of a cuboid is always an integer and is always even.

For example, a cuboid with l = 2, w = 1 h = 1 has a surface area of 10:


2 × ( 2 × 1 + 1 × 1 + 1 × 2 ) = 10
2 × ( 2 × 1 + 1 × 1 + 1 × 2 ) = 10


The minimum surface area a cuboid may have is 6 - namely one for which the '''l''', '''w''', and '''h''' measurements are all 1:
Notice there is no configuration which will yield a surface area of 8.


⚫
2 × ( l × w + w × h + h × l )
In fact, there are 16 even integer values greater than 6 and less than 1000 which can not be the surface area of any integer cuboid.
⚫
2 × ( 1 × 1 + 1 × 1 + 1 × 1 ) = 6


Notice that the total surface area of a cuboid is always an integer and is always even, but there are many even integers which do not correspond to the area of a cuboid. For example, there is no cuboid with a surface area of 8.


;Task
;Task
* Find and display the even integer values that can not be the surface area of a regular, integer, rectangular, cuboid, larger than 6 (the minimum cuboid area) and less than 1000.
* Find and display the sixteen even integer values larger than 6 (the minimum cuboid area) and less than 1000
that can not be the surface area of a cuboid.



;See also
;See also
Retrieved from "https://rosettacode.org/wiki/O%27Halloran_numbers"