This discussion is now closed.

Check out other Related discussions

You are not yet ready for such a problem

J.F.N

Two positive integers are chosen. The sum is revealed to logician A, and the sum of the squares is revealed to logician B. Both A and B are given this information and the information contained in this sentence. The conversation between A and B goes as follows:
B : " I can't tell what the two numbers are."
A : " I can't tell what the two numbers are."
B : " I can't tell what the two numbers are."
A : " I can't tell what the two numbers are."
B : " I can't tell what the two numbers are."
A : " I can't tell what the two numbers are."
B : " Now I can tell what the two numbers are."
What are the two numbers?

Scroll to see replies

8 and 9.

...anyone willing to explain this one?

Reply 3

Plummie

i really don't get it, there's no information to get the numbers from!!

Reply 4

Dilute

I think it's something like person B knows that after there are more than 3 combinations to A's information, while A knows the same about B's information.

Reply 5

super_baros

Exile

8 and 9.

how?????!!! :confused:

Reply 6

Exile

The first line really tells you almost everything giving you need to get range of possible answers. Whilst the second line A narrows it down to only 2 numbers.You need to create a table of 'sum' and 'sum of squares' and you will find that the sum is 17 and the 'sum of squares' is 145, hence two values 8 and 9.

Theres real logic involved in here, dont give up to easy!

Reply 7

Piggy

Sorry for being thick but how does " I can't tell what the two numbers are." give a range of possible answers when there are no numbers?!

Is it that for each possibility of two integers that add up to what A knows, A needs to work out how many possibilities for each of those that B could ahve, and B does the same? When they both know it's been "maxed out" they can find it?

Reply 10

Piggy

But how can they know without giving anything away and just repeating what each other are saying?

--------------

Oh...i'm sort of beginning to see :smile:

Ignore me whilst i spill my brains out on this one

Reply 11

sebbie

but one of the numbers could be 8billion or some other random number?

Reply 12

KAISER_MOLE

Took about 5 minutes for me to see what was going on, then took another 15 minutes to go through the stages, adding squares up to a certain value to see if they equal....I like how it works, I really do...and agree with the answer Exile gave....distracted me from Chemistry revision though >.< (then again, why am I looking on this forum if I wanted to revise :p:

)

Reply 13

super_baros

I'm trying to understand it.. but I'm failing quite spectacularly...... Do I have to have any idea about logic?... or is it just common sense.?... :confused:

Reply 14

Dekota

super_baros

I'm trying to understand it.. but I'm failing quite spectacularly...... Do I have to have any idea about logic?... or is it just common sense.?... :confused:

Higher-Thinking common sense.

Or just Decision Maths.

Reply 15

BCHL85

lolzzzz Know-Don't know game???

Another famous one, probably easier than this one
2 integers are chosen in range [2, 100]. The product of them is given A, the sum is given to B. They both know the range of the numbers.
A: I don't know what the sum is.
B: I knew that you didn't know. I don't know either.
A: Now I know what's your sum must be
B: Likewise, I figure out your product now
What are the numbers?