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Omni-MATH / Two mathematicians, Kelly and Jason, play a cooperative game. The computer…

Problem

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problem

Two mathematicians, Kelly and Jason, play a cooperative game. The computer selects some secret positive integer n<60n<60 (both Kelly and Jason know that n<60n<60, but that they don't know what the value of nn is). The computer tells Kelly the unit digit of nn, and it tells Jason the number of divisors of nn. Then, Kelly and Jason have the following dialogue: Kelly: I don't know what nn is, and I'm sure that you don't know either. However, I know that nn is divisible by at least two different primes. Jason: Oh, then I know what the value of nn is. Kelly: Now I also know what nn is. Assuming that both Kelly and Jason speak truthfully and to the best of their knowledge, what are all the possible values of nn?
Plain-text mathematical notation (without MathML)
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?
Original LaTeX notation
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 $n$?

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Source and history

task_id
036c0acd-b15e-568c-b36f-60cc2e5866c8
task_key
test--036c0acd-b15e-568c-b36f-60cc2e5866c8
task_revision_id
1
config / split
/ test

Official source

initial import