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The assignment shouldn't be specific to a certain problem set.
It should challenge the candidates fundamentals and his grasp on the most pivotal concepts centred around Algorithms and Data Structures.
For problems you can refer to HackerRank and Top Coder for some cool assignments
1) Build a calculator - go onto scientific for a harder challenge.
2) String Manipulation projects - so substrings, palindromes, comparison, splits etc.
3) Reminder App
4) Alarm App
5) Simulator games of favorite sports
Fibonacci series, towers of hanoi, the number factorial and get the number from the keybourd,
the first assignment should depend on the program you are teaching, for example if it a Matlab then starting learining how to do math and cauclation on it
and if it something like C++ then starting with variables would be a good idea
Depends on the field he wants to dive in, a web developer would be asked to make a small web app, a game developer can make a small game, after all practice is the key no matter what.
try something simple and play with it by adding more simple features to it ...
like :
a program that prompts the user to enter anything and processes it and get interesting results out of it