MathDB

A group of n friends wrote a math contest consisting of eight short-answer problem

S_1, S_2, S_3, S_4, S_5, S_6, S_7, S_8

, and four full-solution problems

F_1, F_2, F_3, F_4

. Each person in the group correctly solved exactly 11 of the 12 problems. We create an 8 x 4 table. Inside the square located in the

i

th row and

j

th column, we write down the number of people who correctly solved both problem

S_i

and

F_j

. If the 32 entries in the table sum to 256, what is the value of n?

Problem Statement