Question 99
Paul Erdős was one of the most prolific mathematicians of all time and was renowned for his many collaborations. The Erdős number of a mathematician is defined as follows. Erdős has an Erdős number of $0$, a mathematician who has coauthored a paper with Erdős has an Erdős number of $1$, a mathematician who has not coauthored a paper with Erdős, but has coauthored a paper with a mathematician with Erdős number $1$ has an Erdős number of $2$, etc. If no such chain exists between Erdős and another mathematician, that mathematician has an Erdős number of infinity. Of the mathematicians with a finite Erdős number (including those who are no longer alive), what is their average Erdős number according to the Erdős Number Project? If the correct answer is $X$ and you write down $A$, your team will receive $\max (25-\lfloor 100|X-A|\rfloor, 0)$ points where $\lfloor x\rfloor$ is the largest integer less than or equal to $x$.