Im not going to claim to be a google form master, but I know form and spreadsheet can connect, so storing your data there and feeding it into your form would be a decent way to go. That in conjunction with a random number API like:
http://www.random.org/integers/?num=1&min=1&max=4&col=1&base=10&format=plain&rnd=new
and you should be good to go. Slam the above URL into an =importData()
cell into a spreadsheet and reference it. This solution comes with a caveat, the google form data update frequency is low, theres a hack to get around it if it is an issue, but for your single user form scenario I imagine you should be good to go.
Here is the exact cell data incase you get hung up:
=importData("http://www.random.org/integers/?num=1&min=1&max=4&col=1&base=10&format=plain&rnd=new")