into how many parts will five random planes divide space?

Question

please explain the answer clearly.....

by the way, the answer is not 32!

Answer 1

I am only using visual techniques and not math theorems here:

The first plane will divide space into 2 parts.

If totally random the second plane will probably not be parallel with the first. This will divide the 2 parts into 4. If it did happen to be parallel with the first, then the space is divided into 3 parts.

The third plane will most likely not be parallel with either of the other two. It would divide the space into 8ths. If it was parallel to either of the other two then the minimum parts is 4 and the maximum is 6 parts.

The fourth plane will most likely not be parallel with any of the first 3, and can divide the space into maximum of 15 parts. The fifth will make that 26. Parallel planes will reduce this number.

The space will be divided into a minimum of 6 and a maximum of 26 parts with 5 planes.

I just found a great description at the site below:

Answer 2

The first 3 planes create 8 regions. (That's easy. Just imagine x, y, and z axes and the 3 planes and 8 regions that they create.)

The fourth plane can pass through 7 of these regions, and divide each into two regions. So this adds 7 more regions to the original 8, for a total of 15.

I'm still working on what happens with the fifth plane. It has to add at least 7 more regions (same reasoning as the fourth plane). But it will certainly pass through more than 7 of the 15 regions (and not more than 14. So the answer is more than 22, but not more than 29. If I figure it out, I'll edit this response.

Answer 3

Yo mama is so fat, when she sat down on a quata, she made bogey pop outta Geoge Washingaton's nose!