# Friends Playing

Author: mathforces
Problem has been solved: 16 times

Русский язык | English Language

A group of 16 friends take turns choosing random integer numbers. The first of them randomly selects the number $a_1$ on the segment $[0,1]$, the second - the number $a_2$ on the segment $[0,2]$, the third - the number $a_3$ on the segment $[0,3]$, and so on. Let the probability that the sequence of numbers $a_1, a_2, ..., a_{16}$ is strictly increasing is equal to $\frac {a}{b}$, where $a$ and $b$ are coprime positive integer numbers. Find the number of divisors of the product $ab$.