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#1 2016-11-25 22:55:38

Mac07
Member
Registered: 2016-11-25
Posts: 1

How do I approach this problem?

A cube of 8cm x 8cm x 8cm is divided into smaller cubes of 1cm x 1cm x 1cm and all the smaller cubes are numbered and arranged to form the larger cube. The smaller cubes are numbered such that the number on the cube represents the smallest volume enclosed by extending the sides of the cube to the outer surface of the largest cube and each cube bears the same number on each surface.
Find the sum of the numbers on the cubes along the two body diagonals of the largest cube.

I'm not able to visualise what's given in the problem.

Any help would be appreciated.

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#2 2016-11-26 09:30:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: How do I approach this problem?

Hi;

At this point I am not sure what you are asking.  What have you done already? That may give me a clue.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2016-11-26 23:37:33

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: How do I approach this problem?

hi Mac07

Welcome to the forum.

Here's my thoughts on this: I'll refer to each little cube by using an whole number coordinate system; so the bottom left front cube is (1,1,1) and the one on its right is (2,1,1).  Behind that is (2,2,1) and so on.

Consider the cube in position (2,3,4).  If I extend its sides to the edges of the large cube I get a cuboid 2 by 3 by 4 so volume 24.  The ones on a diagonal will have coordinates (a, a, a) where a is a number from 1 to 8 inclusive.  The one at (4,4,4) will, when extended,  make a cube 4x4x4.  The one at (5,5,5) will make a smallest volume that is also 4x4x4 (go to the shortest outside edge).

Hope that helps smile

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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