Quant Salary

First, quant #1 selects a random number \(X\) and adds it to his own salary, yielding \(\,S_1 + X\). He passes this total to quant #2, who adds her salary to get \(\,S_1 + X + S_2\). This running sum continues around the group, with each of the remaining quants adding their own salaries in turn, until the final total \(\,S_1 + S_2 + \cdots + S_8 + X\) returns to the first quant. Because only the running sum is seen by each person, no one can deduce anyone else’s exact salary. Finally, quant #1 subtracts his original random number \(X\) from the total, leaving \(S_1 + S_2 + \cdots + S_8\). Dividing that sum by \(8\) yields the group’s average salary without disclosing any individual amounts.