O'Halloran numbers: Difference between revisions

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{{draft task}}
 
For this task, athe term "cuboid" ismeans a regular 3-dimensional rectangular object, with six rectangular 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.
 
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. AFor cuboid will always have an even integer surface area. The minimum surface areaexample, a cuboid maywith havel is= 6;2, onew where= the1 '''l''',h '''w''',= and1 '''h'''has measurementsa aresurface allarea 1of 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
 
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
* Find and display the sixteen 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.
that can not be the surface area of a cuboid.
 
 
;See also
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