The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Math Topics » geometry.puzzles

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Brain teasers
Replies: 2   Last Post: Jan 20, 1998 10:28 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Alan Lipp

Posts: 41
Registered: 12/6/04
Re: Brain teasers--SPOILER
Posted: Jan 16, 1998 1:56 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Fri, 16 Jan 1998, Lilly Sun wrote:

> Some unit cubes are put together and form a larger cube, and then
> some of the faces of this cube are painted. After the paint dries,
> then the larger cube is disassembled into the unit cubes and there are
> 24 of these have no paint on any of their faces.
> Question: How many faces of the larger cube were painted?

If all the outer cubes of a 5x5x5 were removed there would be 27 unpainted
cubes inside . . . so clearly the large cube has side less than 5. If
none of the faces of a 2x2x2 cube were painted then only 8 cubes would be
unpainted. So the large cube has either side 4 or side 3. If even one
side of a 3x3x3 were painted then only 18 unpainted cubes would remain.

Therefore, some faces of a 4x4x4 cube were painted.

A 4x4x4 has a core of 8 unpainted cubes with 56 cubes lying on the
surface and we must color all but 16 of them. So the problem is: how to
paint 40 of the face cubes of a 4x4x4 cube.

The solution: paint any three faces which do not meet at a corner.


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.