There are two natural numbers $m$, $n$ greater than $1$: their sum does not exceed
$100$. Now Sarah knows the sum $s = m + n$, and Paul knows the product
$p = m *n$ They have the following dialogue:

```
Paul: I don’t know what m and n are.
Sarah: No, I knew that you didn’t know.
Paul: Oh, but now I do know!
Sarah: And so do I!
```

What are $m$ and $n$?

Question

There are two natural numbers $m$, $n$ greater than $1$: their sum does not exceed
$100$. Now Sarah knows the sum $s = m + n$, and Paul knows the product
$p = m *n$ They have the following dialogue:

```
Paul: I don’t know what m and n are.
Sarah: No, I knew that you didn’t know.
Paul: Oh, but now I do know!
Sarah: And so do I!
```

What are $m$ and $n$?

parthkohli · Answer

I love these riddles.

parthkohli · Answer

Paul means that there are two or more ways to express $p$ as a product of two factors.
Sarah means that there are two or more ways to express $s$ as a sum of two numbers.

There must be an intersection of those two.

I'm thinking about the last two lines.

ikram002p · Answer

i dont speak english :P

rational · Answer

Exactly! From the first statement one thing that we can infer is that the numbers m and n cannot be primes simultaneously.  I find this question both fun and tough too !

ikram002p · Answer

i will wait until  someone reveal the dialog lol

rational · Answer

If it helps, this problem is harder than it seems...

ikram002p · Answer

i feel so

ikram002p · Answer

ok so paul mean p=m*n not unique means they are not both prime (else would be unique)
also means m does not equal n^2

parthkohli · Answer

what's the name of this tool?

mimi_x3 · Answer

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