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Internal & External (Posted on 2003-05-09) Difficulty: 2 of 5
Side-tracked from a slightly related problem, I derived this general set of attributes:

{8, 12n, 6n^2, n^2, n}.

The first 5 situations of this generalisation are:

[8, 0, 0, 0, 0],
[8, 12, 6, 1, 1],
[8, 24, 24, 4, 2],
[8, 36, 54, 9, 3],
[8, 48, 96, 16, 4].

What does this set of attributes describe?

(Attributes #1 & #4 may provide clues. Also, take note of the Title.)

  Submitted by brianjn    
Rating: 3.1667 (6 votes)
Solution: (Hide)
This describes the number of 1x1 cubes within a larger cube.

Visually, if the outer surface of a cube, greater than a 1x1 cube, is coloured, then the attributes represent how many 1x1 cubes are coloured as:

1. 8 vertex cubes
2. edge cubes; 2 faces coloured
3. face cubes with only 1 face coloured
4. those internal cubes which are not coloured, and
5. the order, or magnitude, of the cube under 'investigation'.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle Thoughts K Sengupta2023-07-18 01:25:26
SolutionSolutionwcaexqdz2004-10-27 12:21:10
All addressedBrian Nowell2003-05-14 19:01:23
re(3): A Painted Cube - Shame on me!Brian Nowell2003-05-14 18:54:31
Some Thoughtsre(2): A Painted CubeBrian Smith2003-05-14 04:34:11
re: A Painted CubeBrian Nowell2003-05-13 18:54:18
Some ThoughtsA Painted CubeBrian Smith2003-05-13 07:11:22
Mmm! More clarity needed.Brian Nowell2003-05-10 17:33:47
re(2): First guess....Jon2003-05-10 08:19:55
re(2): ok then.....Lewis2003-05-09 21:38:44
Hints/Tipsre: First guess....Brian Nowell2003-05-09 21:13:00
QuestionQuestion about questionGamer2003-05-09 09:52:26
re: First guess....Jon2003-05-09 09:39:52
First guess....Brian Smith2003-05-09 09:17:38
re: ok then.....Jon2003-05-09 09:04:05
Questionok then.....Lewis2003-05-09 08:56:48
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