Prove existence of different programs printing each other code
You maybe know the recursion theorem. It implies, that you can assume that you have a procedure called get_your_own_codeif your programming language is at least as powerful as a Turing machine.

Now do the following

Progr. A
w=get_your_own_code
print "print "+w


Note that some code is hidden in the subroutine of get_you_own_code. So we assume the complete source code is a string called source_code_of_A.

Progr. B
print source_code_of_A


Program A prints:

  print source_code_of_A


Program B prints

  source_code_of_A