37543

8.

Here is the link to my blog:

(it has my answer and working out):

http://matthewa.blogs.takp.school.nz/2013/01/23/how-many-dots-can-you-f…

I worked for 15 minutes trying stuff, and finally I came up with 8. I double-checked it for 15 minutes, and finally I found out that there were no squares.