carl has a 4 inch cube wrapped in foil. he wants to cut it into 1 inch cubes. how many strokes of the knife will he make? how many 1 inch cubes will he have? ho

Question

Don't know where to start :(

Answer 1

Well, find a 4x4x4 Rubik's Cube or look at the picture at the Toys-R-Us web site:
     http://www.toysrus.com/buy/brain-teasers/rubik-s-cube-4x4-5011-2267476
 
First, the width is 4 and the length is 4 and the height is 4, so there are 64 little cubes.  You should verify that by looking at the picture.
 
Then, look at the top.  With 3 cuts one way and 3 cuts the other way, we have 16 tall columns.  Then, only 3 more cuts and there are 64 little cubes (again, study the picture !).
 
 
From the picture, you can count each of the 8 corners that will still have foil on 3 sides.
 
Then, there are 2x2x2=8 hidden little cubes that will have no foil at all.
 
Now, there are 4 little cubes in the center of each of the 6 surfaces that will have foil on only 1 side  (4x6=24).
 
That leaves 64-8-4-24 = 28 little cubes that have foil on two sides -- or, you could count them.

Answer 2

So currently you have a 4 x 4 x 4 in cube.

 

Let's first make three cuts so you end up with 4 x 4 x 1 rectangular pieces.

 

Assuming the pieces are still in the shape of a cube (you did not move the pieces after cutting them), you turn the pieces 90 degrees and make another three cuts. Now you will end up with 16 4 x 1 x 1 pieces.

 

Now, assuming the pieces are still in a cube, rotate the cube and make another three cuts to get 64 1 x 1 x 1 pieces.

 

So you have made 9 cuts total and now have 64 pieces. This solution is assuming you can line up pieces and cut multiple pieces at the same time.