How do I test a ranking system?

Let us assume we have 3 students in a class with the below marks

   <table border='1'>
    <tr><td></td><td>Mathematics</td><td>English</td><td>Science</td></tr>
    <tr><td>John</td><td>60</td><td>40</td><td>70</td></tr>
    <tr><td>Mark</td><td>30</td><td>90</td><td>40</td></tr>
    <tr><td>Alice</td><td>60</td><td>60</td><td>70</td></tr>
    </table>

Normally the rank is decided by adding all three marks and sorting the total in descending order.

Looking at the above table, the rank would be Alice, John, Mark. If there exists a system that takes student marks as input and gives out the rank sequence as response, then how do I certify that the system returns student ranks in sequence for all sorts of possible data?

What should be the approach to test such a system? Generating all possible combinations of data would be exhaustive when the number of students and subjects increase.