Edit. I thought I had the total solution but I was wrong. Below is a partial solution.
This is what you want to do. First set the ownership of the example directory to TheUser:users.
chown theuser:users example
Then set the sticky bit for the group that owns the directory.
The 4 in the above permission string will force all files created in the example directory to be owned by the users group.
You may not need the sticky bit on the "others" permissions. I'm not sure.
Next you want your user accounts to have their umask set to 740. This next line of code has to go into a login script like /etc/profile.