MathDB

Two mathematicians, Kelly and Jason, play a cooperative game. The computer selects some secret positive integer

n < 60

(both Kelly and Jason know that

n < 60

, but that they don't know what the value of

n

is). The computer tells Kelly the unit digit of

n

, and it tells Jason the number of divisors of

n

. Then, Kelly and Jason have the following dialogue: Kelly: I don't know what

n

is, and I'm sure that you don't know either. However, I know that

n

is divisible by at least two different primes. Jason: Oh, then I know what the value of

n

is. Kelly: Now I also know what

n

is. Assuming that both Kelly and Jason speak truthfully and to the best of their knowledge, what are all the possible values of

n

Problem Statement