Elementary POW, March 17-21, 1997

Elem POW Problems || March - June '97 Problems || Elem POW Main Page

You have a three-inch cube painted red (length, width and height are each 3 inches). See if you can answer the following questions about the cube:

1. How many cuts will it require to divide the cube into one-inch cubes?
2. How many cubes would you have?
3. How many cubes would have four red sides?
4. How many cubes would have three red sides?
5. How many cubes would have two red sides?
6. How many cubes would have one red side?
7. How many cubes would have no red sides?

As you answer parts c to f of the problem, try to think of a way of explaining where the cubes in your answer would be. You might devise a numbering system or another method so that the reader will understand which cubes you are refering to. Here's an example:

top layer
1 2 3
4 5 6
7 8 9

middle layer
10 11 12
13 14 15
16 17  18

bottom layer
19 20 21
22 23 24
25 26 27

This week's mentor is Diane Nolan.

Correct Solutions submitted by:

Highlighted Solutions

[Privacy Policy] [Terms of Use]

Home || The Math Library || Quick Reference || Search || Help 

© 1994-2012 Drexel University. All rights reserved.
http://mathforum.org/
The Math Forum is a research and educational enterprise of the Goodwin College of Professional Studies.