MathDB

A math contest consists of

9

objective type questions and

6

fill in the blanks questions. From a school some number of students took the test and it was noticed that all students had attempted exactly

14

out of

15

questions. Let

O_1, O_2, \dots , O_9

be the nine objective questions and

F_1, F_2, \dots , F_6

be the six fill inthe blanks questions. Let

a_{ij}

be the number of students who attemoted both questions

O_i

and

F_j

. If the sum of all the

a_{ij}

for

i=1, 2,\dots , 9

and

j=1, 2,\dots , 6

972

, then find the number of students who took the test in the school.

Problem Statement