Question 824014
It seems a linear algebra problem.  Six students, six different questions, all asked of every student.  Each question is of a different point value than other questions.  The point value of each question is a variable, and you have six variables.


A matrix might be like this:
1, 1, 0, 1, 1, 0, 26
0, 1, 1, 0, 0, 1, 21
0, 0, 1, 1, 1, 1, 32
1, 1, 0, 1, 0, 1, 26
1, 0, 1, 0, 1, 0, 21


Unfortunately, the last row in the reference does not give the total points as known so you only have FIVE equations; not six.


I'd rather resort to software; regardless of any skill within linear algebra.  Try the purdue website's matrix calculator or meta-calculator site.