Fun problem at bottom! A CT scan is also sometimes known as a Cat scan. Black, white and grey images. To understand a CT scan we need to understand a X-ray machine.
X-Ray Machine
An X-ray machine sends out a beam of high energy rays that travels through the air and then comes in contact with the body. The beam passes through the body and depending on the tissue only some of it makes it through to the other side. This amount that makes it through then leaves either a black mark (all of the beam made it through), a white mark (none of the beam made it through) or some grey scale in between. In particular
- Soft tissue, such as skin and organs, cannot absorb the high-energy rays, and the beam passes through them.
- Dense materials inside our bodies, like bones, absorb the radiation.
An X-ray image showing dense bones (white), soft tissue (grey) and blank space (black)
CT Scan
Now that we know about how an X-ray works we can apply this to a 3D image. If you take an image at every direction in a circle surrounding the body you will get a simultaneous problem. The sum of all the tissue in one direction is given a value from zero to 1 and eventually you can work out each individual cell. The more images you take the better the resolution. If you only took 4 images you could only work out 4 individual chunks.
CT Scan Machine Image from Wiki
A Fun Problem
Below is an image for a fun problem. Every "cell" (inner white box) is either black or white. The number along the top row give you the total number of black cells in each column. The numbers down the left side of the box gives you the total number of black cells in each row. The numbers in the "L" shape starting on the left give the diagonals in one direction and the rest give you the number in the opposing diagonal direction.
Your problem if you choose to accept it!
I got the idea from a conference I went to but adapted it for you guys. If you get the answer please do not spoil it for others.