Can you guess the numbers?

Somehow I feel they should be 97 and 1

because when ash said she(/he) couldnt find and mArO was excited that he(/she knew that ash would not find it), It actually means that marO could find them straightaway. and when ash sees maro excited, she already knows the sum is 98. and now she can guess why maro is so excited(he probably knows the answer,

I feel confused now.

PS: Both Ash & MaRo are 'He' and moderators of CE Forums 😁

We want a confusion-free answer.

... and I used to think we have some smartest brains from all over the world. But I was wrong. We do not have smartest people. We just can't crack a simple puzzle!

PS: Does that hurt your ego? 😁

I'm still waiting for the brainy CEan who can crack this!

actually both of them don't know those numbers😉.....just they are bluffing each other 😁

😁........

anuragh27cronyactually both of them don't know those numbers😉.....just they are bluffing each other 😁

😁........

What a ... lame answer. :sleeping:

Sorry !

If you think hard, you'll see that the numbers can be guessed!

srry for those lame answer......i think answers are i) 2,2 or ii)2,3

Assumption : Both numbers should be more than 1

since Ash and Mac knew sum and other the product...but they never exchange information abt sum/product....

if numbers are 2,2

Ash knows 4....but basic priciple is both numbers are more than one so
1,3(it differs because...one number is equal to one)
2,2

and Mach know 4...
so it can be
1,4 (it differs because...on number is equal to one)
2,2
............................
if numbers are 2,3

Ash knows 5....but basic priciple is both numbers are more than one so
1,4(it differs because...one number is equal to one)
2,3

and Mach know 6...
so it can be
1,6 (it differs because...on number is equal to one)
2,3

[Update]: 1 < x < y and x+y < 100 [x,y are the numbers].

But, is the answer, right? 😁

Think harder!

[PS: I sincerely & honestly believe that xy cannot be the product of two distinct primes, for then Ash could deduce the numbers.]

Or, am I just wrong here? 😁

yeah then 2,3 is the right answer....which can be gussed by both ....even with out transferring peices of information.....

and also satisfies the condition too

1<(X=2)<(Y=3) 😁

[PS: If the both numbers are not disitinct primes then...there's possibility that Mac get's confused with correct pair numbers since it leaves the scope for more than one possibility of xy combination.and yes we can deduce the numbers even they are not distinct primes...if the basic condition is modified as 1<x<=y then answer can be X=Y=2]

134😁

ntr_youngtiger134😁

What's that?

@The_Big_K ...plzz comment on my answer in the recent post.......
whether my solution is right or not

anuragh27crony@The_Big_K ...plzz comment on my answer in the recent post.......
whether my solution is right or not

Okay, here's my comment -

If Ash knew the that the sum of numbers is 5. Then he'd have following options in his mind -

(1,4), (2,3)

But, he knew the numbers are both greater than one. Then, he'd not have said the following -

Ash: I can't determine what are these numbers.

That is, Ash could not determine the numbers for sure!

So, unfortunately, we need some hard thinking over here, I think. 😲

big_k answer please.......can't wait...for long time

Sorry sire, the answer will not come. Its open for the non-quitters 😉 . Come on, try harder!

😁

Interesting - I'm not sure the problem is correctly posed, since it is obvious given only the sum of the two numbers that you would not be able to derive a solution. Adding that a solution "should" be possible, the assumption would be that you only consider unique values, which for sums gives 4 values: 5, 6, 98 and 99.
Based on a=x+y and b=xy, then x=b/y and y2-ay+b=0, so y=(a+sqrt(a2-4b))/2. The list of integer values of this function for 1<x,y<51 has a number of pairs of results, which makes it diffcult to see how the additional data that there isn't a unique result, helps produce a unique result. Please check the question is accurate.

barryn,

Are you completely ignoring the dialogue between Ash & MaRo? Its there - and it's got all the clues you need to crack the problem.

CEan - #-Link-Snipped-# was making a good progress, but looks like he's given up 😉

Think harder.

@Big_k....
Ash: I can't determine what are these numbers.
MaRo: Ah, i knew you wouldn't be able to do this.

i can't deduce the significance of these dialouges in solving problem....

Hint please....

Are you sure you don't mean their PRODUCT is less than 100?? Otherwise I don't think this is solvable, because there are many solutions...

The conditions have been mentioned and they haven't changed so far. Shall I post the answer or wait for few more days?

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?😎

is this correct,big_k?

No. It is not.

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

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

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.

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

the answer is 3,4

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

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).

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

any two prime nos whose product is less than 100 should be the answer.
ex: 2,5
3,5
let me know whether its right or not.

Guys, when you post your answer, also post a detailed explanation and the methodology you used to arrive at your [so far incorrect 😁 ] answer(s).

My first post as a
😕
not given that x & y are unique?
I'll assume this.
x,y >1
1. Ash says he can't deduce the numbers from the sum
obviously very difficult as sums are not unique.
except for 5(2,3) & 6(2,4)
after 7 its not unique anymore (2,5), (3,4)

2. On hearing this Maro can only deduce that sum is >6
but Maro has the product and products have lesser possibilities, still difficult for him to conclude the numbers.
consider both distinct primes: if this was the case Maro would have been able to find the numbers. Eg 13*11=143 only 13 & 11 and 143 & 1 give this product and since x,y>1 only 13,11 fulfill the condition.

3. On hearing Maro state his failure, Ash now knows that the 2 numbers are not prime & their sum.
But now he has guessed it!

What is the least number for which he could guess this? A sum that has only 1 unique combination (which are not primes), and other combinations are primes since he's just eliminated them at step 2.

7
(2,5) (3,4)
note that if the numbers were 2,5 maro wld have been able to tell the numbers from the product(10)

10
(2,8) (3,7) (4,6)
note that if the numbers were 2,8 maro wld have been able to tell the numbers from the product(16)--same for 21
eliminate first 2 - numbers are 4,6

😕
I think the answer(sum) can be 7, 10 and lots of others but I guess for now I can't do better than taking the least answer as mine.

So I go with 3 & 4 as the numbers, 7 as the sum and 12 as product

let 2 nos be a & b,thn Ash has x=a+b n Maro:y=a*b
so y=a*b=(x-b)*b=xb-(b*b)
Satisfying this condition s obviously a=4 and b=2...


Please lemme know if there s any correction....

:sleeping:


Wake me up when you get the right answer.

@Big_K....

This is my guess.. is the right answer (49,50) ???

If it's right i'll post the explination

anuragh27crony@Big_K....

This is my guess.. is the right answer (49,50) ???

If it's right i'll post the explination

:sleepy: :sleeping: :sleepy:

Sorry?

gravz84My first post as a
😕
not given that x & y are unique?
I'll assume this.
x,y >1
1. Ash says he can't deduce the numbers from the sum
obviously very difficult as sums are not unique.
except for 5(2,3) & 6(2,4)
after 7 its not unique anymore (2,5), (3,4)

2. On hearing this Maro can only deduce that sum is >6
but Maro has the product and products have lesser possibilities, still difficult for him to conclude the numbers.
consider both distinct primes: if this was the case Maro would have been able to find the numbers. Eg 13*11=143 only 13 & 11 and 143 & 1 give this product and since x,y>1 only 13,11 fulfill the condition.

3. On hearing Maro state his failure, Ash now knows that the 2 numbers are not prime & their sum.
But now he has guessed it!

What is the least number for which he could guess this? A sum that has only 1 unique combination (which are not primes), and other combinations are primes since he's just eliminated them at step 2.

7
(2,5) (3,4)
note that if the numbers were 2,5 maro wld have been able to tell the numbers from the product(10)

10
(2,8) (3,7) (4,6)
note that if the numbers were 2,8 maro wld have been able to tell the numbers from the product(16)--same for 21
eliminate first 2 - numbers are 4,6

😕
I think the answer(sum) can be 7, 10 and lots of others but I guess for now I can't do better than taking the least answer as mine.

So I go with 3 & 4 as the numbers, 7 as the sum and 12 as product

lol..such a long post...
no comments??
My answer was that there are no unique numbers that the two have thought of and the least possible combination is (3,4)
At least write if the line of thought/ approach is right...
and what is the mistake..
simply posting the solution is of no use, i agree; so I would appreciate if some discussion could ensue as to each person's solution and approach!
anyone??

Raj_rising_engilet 2 nos be a & b,thn Ash has x=a+b n Maro:y=a*b
so y=a*b=(x-b)*b=xb-(b*b)
Satisfying this condition s obviously a=4 and b=2...


Please lemme know if there s any correction....

To advance what I just posted, I'll analyze some solutions suggested by others.
Raj,
the two are not communicating the results ie sum and product that they have been given. They only express whether they have independently concluded the 2 numbers.
What you have stated, requires the knowledge of both sum and product. Plus you can substitute any 2 given numbers in that equation and get the same result. obviously all numbers fulfill this:
y=a*b=(x-b)*b=xb-(b*b)

In statement 1, Ash(guy given the sum of the 2 numbers) says he can't find out.
In statement 2, Maro(guy given the product of the 2 numbers) says he can't find out.
In statement 3, Ash now says he has found out the solution.
In statement 4, Maro now says he has found out the solution.
there must have been extra information for Ash between statement 1 & 3 which is what you should be looking at-since there is no external information the extra information that has helped him solve the puzzle is statement 2.
Similarly for Maro.

crazyashany two prime nos whose product is less than 100 should be the answer.
ex: 2,5
3,5
let me know whether its right or not.

😒
If the 2 numbers were both primes then the product is unique, right?
ie there is only one way to factorize 15 3*5, only 1 way to factorize 55 11*5, so the person who knows the product would instantly know the 2 numbers (both numbers, it is assumed, are distinct and greater than 1) but it is not so so the solution based on both primes is incorrect in my opinion.

MungutiI 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

it is indeed the first product which satisfies but there are others that have 2 possibilities that are solved by Ash only after the 1st 2 statements are made.
So in my opinion there are many such solutions but 3,4 is the least one.

nos r 4 and 3
sum - 7(Ash)
product - 12 (MaRo)

i believe that the product of the numbers should be 16
and the sum of the numbers is 8


so maro has the product (16)
he has got 2 possibilities of numbers (2,8) and (4,4)
the respective sums are 10 and 8
for both the sums he is sure that Ash wouldnt know the correct answer

but when ash realizes that maro knows that she cant guess the nos
and she knows the sum is 8
she thinks of the possibilities
(2,6) (3,5) (4,4)
for (6,2) product is12
for (3,5) product is 15
for (4,4) product is 16

15 cant be the product as in that case maro would have known the nos
12 cant be the product as in that case maro had possibilities (3,4) (2,6)
giving the sums as 7 and 8. in that case maro couldnt have said that he knew that ash wouldnt know the answer

so ash realizes that the nos are (4,4)

when maro comes to know that ash knows the answer he rethinks over his possibilities (2,8) and (4,4,)
for (2,8) the sum was 10 for which ash couldnt have told the correct answer
so maro also realizes that the nos are (4,4)

Okay, those who think their answer is right, please prove that other answers are wrong.

This is oh-so-interesting!

I have got the answer and the solution too... But I'm going to wait till people try their level best.

mayurpathakI have got the answer and the solution too... But I'm going to wait till people try their level best.

I *HOPE* you don't have the *WRONG* answer

Yeah, I believe we should wait till someone from other galaxy cracks this puzzle for us and tells everyone why his/her answer is THE RIGHT ANSWER.

No I'm sure of the answer now. 😀

But let me wait a while

mayurpathakNo I'm sure of the answer now. 😀

But let me wait a while

I still think given the constraints(which are quite wide) and assuming that the 2 numbers are unique, there can still be multiple answers and everyone's giving 1 of those multiple solutions.
Still 3,4 is the least possible solution in my opinion.
😕
Hope you guys give out the answer and a satisfactory solution shortly.

I Have Guessed. 😀

the answer is 13 and 4.
sum=17
prod.=52
when first friend said initially tht he cant fine the numbers,it implied that the product didnot have
CASE (1)-any absolute factors(factors except 1 and the number itself are called absolute factors,e.g. in case of 10: 1 and 10 are not absolute factors,but 2 and 5 are) or
CASE (2) any power of prime i.e 8(2x2x2) or 27(3x3x3) or
CASE (3) product of 2 primes.
now when 2nd one admitted his failure to find out the numbers it meant that none of the possible values of the sum can be such that their product has exactly 2 numbers whose product gives the given value.
now in "higher algebra-silva" an empirical rule is given which helps us find such numbers.we can restrict our list to small numbers since we know the sum of the two numbers is less than 100.

after this both can get the answer by the given method

make a list of all left possible combinations of numbers and just check which number can b expressed in one form only.
we get only 2 possible values:13 and 4.

*thinking* Hmmm... well. Any other explanations?

Is there a shorter and simpler explanation for this one?