What to do during an MRI

Had a second set of MRIs today.  The doctor wanted to see whether the tumor had spread up or down the spine, so he order a thoracic (t) spine and a cervical (c) spine mri.

This time, I left my eyes closed most of the time, as last time, I came out dizzy and had to spend some time laying down.  This time I was all right.

So, if you're like me, which you're probably not, what do you do during an hour-and-a-half MRI?  You invent and solve math problems.

(I did all the coding in my head that there was to do on Monday.  Problem with coding in your head is you have to go do it on the computer, which takes longer.)

So, here's what I came up with today.

Suppose you can put multiple MRI scanners in one room (which I don't think you can).  The scanner takes up 2 vertical units of area.  In order for a scanner to be present, it has to be surrounded by empty units of area.  Sorry, I'm too lazy to make pictures.

So, for one scanner to be in one room, you need 3 units wide by 4 units tall. 

For each subsequent scanner, you need 2 additional units horizontally, or 3 additional units vertically.

Question: Given N units of area, what is the optimal arrangement of scanners?

I had solved this up to the point where I would have to differentiate 1/x, at which point I couldn't keep track of all of it in my head anymore.