Question 40
Mable and Nora play a game according to the following steps in order.
(1) Mable writes down any $2015$ distinct prime numbers in ascending order in a row. The product of these primes is Mable's score.
(2) Nora writes down a positive integer.
(3) Mable draws a vertical line between two adjacent primes she has written in step (1), and compute the product of the prime(s) on the left of the vertical line.
(4) Nora must add the product obtained by Mable in step (3) to the number she has written in step (2), and the sum becomes Nora's score.
If Mable's and Nora's scores have a common factor greater than $1$, Mable wins. Otherwise Nora wins.
Who has a winning strategy?
(1) Mable writes down any $2015$ distinct prime numbers in ascending order in a row. The product of these primes is Mable's score.
(2) Nora writes down a positive integer.
(3) Mable draws a vertical line between two adjacent primes she has written in step (1), and compute the product of the prime(s) on the left of the vertical line.
(4) Nora must add the product obtained by Mable in step (3) to the number she has written in step (2), and the sum becomes Nora's score.
If Mable's and Nora's scores have a common factor greater than $1$, Mable wins. Otherwise Nora wins.
Who has a winning strategy?