Here are links to some programming problems (and solutions) that might be suitable as examples, exam problems, simple exercises and assignments.
Euler problem #5
2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.What is the smallest number that is evenly divisible by all of the numbers from 1 to 20?
Euler problem #16
The sum of the digits in 2^15^ is is 3 + 2 + 7 + 6 + 8 = 26. What is the sum of the digits in the number 2^1000^?