Can you guess the numbers? - Page 3

sreedu

the product is never a prime number becoz one of the numbers will be 1.so the product will be such a number which has 2 factors other than 1 and the no: itself.so product will be <=10.it can't be 1,2,3,4,5.if product is 6 the numbers are 2&3.so sum is 5.ash may think numbers are (1,4),(2,3).so he needn't have any confusion.so the product is nt 6.its nt 7.if prod is 8 the sum is 6.so numbers can be (2,4),(3,3).here too no confusion.product can't be 9.

so product is 10.sum is 7.numbers can be (1,6),(2,5),(4,3).confusion arises at (2,5),(3,4).but since maro don't hav any confusion,ash can confirm the numbers to be 5,2
is this correct,big_k?

The_Big_K

Quote:

is this correct,big_k?

No. It is not.

ummeshh

Aaahh...
I cant get any clue from their dailogues..
If my guess is right., then it would be 4...

Munguti

The numbers range from 2 to 98. Their sum is not unique otherwise ash would have known them(i.e. their sum is anything from 6 to 100, since 1+1=2
2+1=3 and none of the numbers is 1
2+2=4 unique
2+3=5 unique
2+4=3+3=6 start of ambiguity
2+5=3+4=4+3=7
2+6=3+5=..........
then ash has a number between 6 and 100

Then from the information Maro has (product of the two numbers) he knows that their sum is ambiguous and therefore we can say he has a rough idea of the two numbers say maybe two unique pairs at most. The number range Maro has is from 8,9,10,12,15....... up to some number that can be determined from a multiplication table with numbers 2-98 on both sides multiplying by each other.

What i am saying is that by generating a multiplication table and an addition table from the range given above we can get a unique solution based on a simple logic that what should be unique(or having at most two equal solutions for different pairs of numbers) is their product.
i didn't have that much tyme but anyone willing to try it should post the findings

The_Big_K

Alright, this should be my last post in this thread; unless of course, no one cracks the puzzle.

Pay attention to the dialog between Ash & MaRo. When I tell them the sum & the product respectively along with the conditions, each one of them has few pairs of numbers ready in their mind before the dialog happens.

Now pay attention: -

Ash also knows possible pairs of numbers MaRo has in his mind. Similarly, MaRo knows Ash has few pairs in his mind. Now starts the elimination game. Ash says "I can't determine what the numbers are". MaRo immediately picks up his clue and understand's Ash's situation (why he could not tell the answer). When MaRo says "I don't know the numbers too", Ash has enough information to eliminate the incorrect pairs - how? he knows if MaRo can't deduce the answer even after knowing that Ash couldn't determine the numbers. So he immediately says "Oh, then I know the numbers".

Now you've enough hints. Think hard.

murali_pclover

Hi Big_K.Can you give the complete question once again.

confounded

the answer is 3,4

Munguti

I think the product given is 12 since it is the first product with more than one option i.e. two 4,3 and 6,2 therefore one can be eliminated. I also think the sum given is seven since it also has two options and one can be eliminated. so i am with confounded

AlanMc · 02:15 AM

Because MaRo said the he KNEW that Ash couldn't determine the numbers, it means that MaRo was able to deduce the numbers from his product, because the product is unique. Because the sum must be less than 100, the numbers must be between 2 and 97 (inclusive). The larger sets of these numbers have unique products, but not a sum less than 100. Because the sum is less than 100 the unique product must be small. However, because Ash was able to determine the answer from realizing MaRo knew he didn't know, it mean that only one of his numbers has a unique product (which he knew it now must have, because MaRo already knows).

anuragh27crony

@Big_k
Does Maro Knew about the condition of x+y<100 ??