Alice and Bob are perfectly logical and super intellegent. Their professor decides to play a game with them, and he tells them: “I have chosen two numbers x and y with 2≤y≤x≤100. I will tell Alice the value of their difference d=x−y and Bob the value of their ratio r=x/y. I stress that the ratio ris an integer, too.”
After the professor has told the difference to Alice and the ratio to Bob, the following exchange occurs:
- Alice: I don’t know the numbers.
- Alice: You might though. Do you know them?
- Bob: No, I don’t know them.
- Alice: Too bad, if you did I would know them too.
- Alice: I still don’t know them though.
- Bob: Me neither.
- Alice: Oh really? Then I do.
- Bob : Dang it; I still don’t.
What is the value of r?
What are the possible values for x and y?
This is how I reasoned:
There are 382 sets with 2 ≤y≤x≤100 where x/y is an integer.
Statement 1 says Alice doesn’t know the numbers.
This means that we can eliminate all sets that have a difference d that only appears once.
357 remain.
Statements 2 & 3 say that Bob doesn’t know them,
so we can eliminate sets that have a ratio r that only appears once.
Statement 4 however says, if it had been one of those sets, then Alice would know the numbers, because in all those sets, y=2.
So d must be one of the d’s that appeared in one of the sets just eliminated.
Only 49 other sets have one of those d’s.
5: Alice still doesn’t know the numbers, so we can again eliminate sets with a unique d.
46 remain.
6: Bob still doesn’t know, so we can eliminate sets with a unique r.
34 remain.
7: Now, suddenly Alice knows the numbers, so d must be unique among the remaining sets.
Only 4 sets remain:
{x=85, y=17, r=5, d=68}
{x=95, y=19, r=5, d=76}
{x=91, y=13, r=7, d=78}
{x=100, y=4, r=25, d=96}
8: Bob still doesn’t know x and y, so r is still not unique.
Only 2 sets remain:
{x=85, y=17, r=5, d=68}
{x=95, y=19, r=5, d=76}
So r is 5 and x,y is either 85,17 or 95,19. Alice knows, but we don’t.
im a fucking shitlord, nigga
UMA 
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