linuxmemes

Yeah, I really liked my prof for some of the programming courses, but also damn him for making us write code on paper in the exams

I would just write down the steps I would take, just some psudocode. It doesn't have to work, it just has to make sense in the style of the language you're talking about.

import random library  
import any GUI/display libraries required for the outcome desired

build array of integers [1..52] (or 0..51 if you're being fancy)
for loop 1..1000
       select random number A 1..52 (or 0..51 if you used that above)
       select random number B 1..52 (or 0..51 if you used that above)
       swap elements in the array A and B
pop first two elements from array
decode at display time what the two numbers represent in terms of playing cards

If the test requires more than that, then they're crazy. The syntax doesn't matter, just that you can logic yourself through the problem.
You can use the IDE, google, or whatever to fill in the specifics. If you wanted me to do that in literally any programming language, once the psudocode is done, you just spend an hour or so looking up the details.

Even the odd numbers stuff? I think interviewers account for nerves and being outside an IDE. You might draw a blank but would you be would be randomly adding things like these did?

for some reason I still needed to know programming on paper so much so that at the university, in class prgramming we had to do the exam on paper. every time. no matter if it was Java or C++...

I strangely enjoyed it, but it still was kinda weird.