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> Then there are the questions that, at first sight, do not seem to have all the information, yet they do. I love the following problem, in a similar vein: Th
by js8 9y ago
> Then there are the questions that, at first sight, do not seem to have all the information, yet they do.
I love the following problem, in a similar vein:
There are two chosen natural numbers x and y, both between 1 and 100. Two smart people, Alice and Bob, are told this fact, and Alice is secretly told x*y, and Bob is secretly told x+y, and they are also told who knows what. Then the following conversation happens:
Alice: I don't know the two numbers.
Bob: I knew you wouldn't know them.
Alice: Now I do know the two numbers.
Bob: And now I do know them as well.
The question is, what are the two numbers?
- t0mbstone 9y ago4 and 13
- lalaland1125 9y agoBefore anyone else gets lost trying to solve this, the parent posted the puzzle incorrectly. The correct limits on the numbers are that: - Each of them is greater than 1, but their sum is less than 100
- bllguo 9y agoStill not all the information according to this link: https://en.wikipedia.org/wiki/Sum_and_Product_Puzzle https://en.wikipedia.org/wiki/Sum_and_Product_Puzzle y > x is the last constraint
- contravariant 9y agoThat constraint is not necessary as the problem only asked for the two numbers, not the values of x and y respectively.