For $n \ge 0$, let $f_n$ denote the $n$th fibonacci number (that is, $f_0 = 0, f_1 = 1$, and $f_n = f_{n-1} + f_{n-2}$ for all $n \ge 2$). what is the greatest possible value of the greatest common divisor of two consecutive fibonacci numbers?

Each person in an it department of 25 people works on at least one of 3 major projects: system security, program implementation, platform development. 10 people work on system security, 13 work on program implementation, and 12 work on platform development. 4 people work on system security and platform development, 5 people work on program implementation and platform development, and 2 people work on all three projects. how many people work on system security and program implementation?