Jump to content

O'Halloran numbers: Difference between revisions

O'Halloran numbers (view source)

Revision as of 16:23, 6 November 2022

222 bytes added ,  1 year ago
m
Restore my task description
m (→‎{{header|jq}}: correct comment)
m (Restore my task description)
Line 1:
{{draft task}}
 
For this task, thefor termour purposes, a "cuboid" meansis a 3- dimensional 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. It will subsequently be referred to simply as a cuboid; but be aware that it references the above definition.
 
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. ForA example,cuboid will always have an even integer surface area. The minimum surface area a cuboid withmay lhave =is 2,6; wone =where 1the h'''l''', ='''w''', 1and has'''h''' ameasurements surfaceare areaall of 10:'''1'''.
 
2 × ( 2l × 1w + 1w × 1h + 1h × 2l ) = 10
2 × ( 1 × 1 + 1 × 1 + 1 × 1 ) = 6▼
 
Different cuboid configurations (may) yield different surface areas, but the surface area is always an integer and is always even.
The minimum surface area a cuboid may have is 6 - namely one for which the '''l''', '''w''', and '''h''' measurements are all 1:
 
A cuboid with l = 2, ×w (= l1 ×h w= +1 whas ×a hsurface +area h × lof )10
▲ 2 × ( 1 × 1 + 1 × 1 + 1 × 1 ) = 6
 
2 × ( 2 × 1 + 1 × 1 + 1 × 2 ) = 10
Notice that the total surface area of a cuboid is always an integer and is always even, but the converse is not true. For example, there is no cuboid with a surface area of 8. It is conjectured, however, that for every even integer greater than 924, there is a corresponding cuboid with that area.
 
There is no configuration which will yield a surface area of 8.
 
There are 16 known even integer values below 1000 which can not be a surface area for any integer cuboid. It is conjectured, though not rigorously proved, that no others exist.
 
;Task
Thundergnat
10,333

edits

Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/333248"
Cookies help us deliver our services. By using our services, you agree to our use of cookies.
More information