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Cube Painting


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#1 StarLord

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Posted 18 August 2014 - 11:23 AM

A big cube is divided into smaller cubes. The middle cubes on all the four edges of the top layer are divided into eight smaller cubes each. The entire is then painted black.


1) How many smaller cubes are painted black on more than 3 faces?
0         4         8         12


2) How many smaller cubes are painted black on only 3 faces?
0         4         8         12


3) How many smaller cubes are painted black on only 2 faces?
4         8         12         16


4) how many smaller cubes are painted on only 1 face?
18         20         22         24


5) how many smaller cubes are not painted black at all?
1         3         6         9.


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#2 bonanova

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Posted 18 August 2014 - 04:27 PM

What is the initial division? 3x3x3? something else? or purposely not given?


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#3 k-man

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Posted 18 August 2014 - 07:30 PM

Spoiler for assuming 3x3x3 initial division

Edited by k-man, 18 August 2014 - 07:30 PM.

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#4 StarLord

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Posted 19 August 2014 - 06:51 AM

@bonanova . purposely not given .


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#5 bonanova

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Posted 19 August 2014 - 05:56 PM

"The middle cubes on all the four edges of the top layer" means (all) the inner (or non-corner) cubes, then.

OK thanks.


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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