Can you guess the numbers? - Page 6

wtf

Is there a shorter and simpler explanation for this one?

gravz84

Quote:

Originally Posted by wtf

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.

I am not sure if you have the right answer or not but you definitely have one mistake in your solution. Might not change the answer though:
The first guy, Ash is given the sum and the second one the product. You took them as the opposite..

The_Big_K

So many engineers, so many answers.

I'm thinking if crazyengineers ever decide to build a skyscraper, we'll never be able to finalize the design.

{Turns on the music player and watches everyone scratch head

}

wtf

the order does matter but when the 'sum' guy said that he cant find the numbers he obviously had ruled out the clause that the sum he has is a number with exactly one possible absolute factor combination(else the other guy would have known the answer) and his assumption was based on the fact that the 'product' guy is not dumb and he had considered the fact that the number can't be product of 2 distinct primes or a power of some prime number.
So in this question the order does not hamper the conditions for solution,assuming that both friends are genius.

gravz84

Quote:

Originally Posted by wtf

the order does matter but when the 'sum' guy said that he cant find the numbers he obviously had ruled out the clause that the sum he has is a number with exactly one possible absolute factor combination(else the other guy would have known the answer) and his assumption was based on the fact that the 'product' guy is not dumb and he had considered the fact that the number can't be product of 2 distinct primes or a power of some prime number.
So in this question the order does not hamper the conditions for solution,assuming that both friends are genius.

Hope you take all this in a sporting spirit.

"
when the 'sum' guy said that he cant find the numbers he obviously had ruled out the clause that the sum he has is a number with exactly one possible absolute factor combination(else the other guy would have known the answer)
"
you have made an extra assumption.. ie the "sum guy" Ash already knows that Maro has stated that he doesn't know the answer.
Of course since this is a theoretical situation, information must flow distinctly as dialogues... maybe at the time ash is making his statement maro already knows the answer but this can be established only when maro makes his first statement.
Also one more thing in your explanation that I take exception to is:
"the number can't be product of 2 distinct primes or a power of some prime number."
the number(s) can definitely be powers of prime numbers!!
8=2^3 and 4=2^2 bt from the product 32 he still can only deduce that the numbers are either (2,16) or (8,4) so they can definitely be powers of prime numbers!!
Also how you get 13 and 4 as the only possible solution escapes me..

clarify--for eg why can't the solution be (3,4), (23,4) and (17,4) just for the sake of elimination by samples..

wtf

y isnt no one replying back?

is this answer wrong?

..plz big k jus temme if this is right,i have my campus connect classes from 5:30...gotta go for that....wont b able to concentrate there if this thing dusnt get out of head.
proud 2 b a

gravz84

Quote:

Originally Posted by The_Big_K

So many engineers, so many answers.

I'm thinking if crazyengineers ever decide to build a skyscraper, we'll never be able to finalize the design.

{Turns on the music player and watches everyone scratch head

}

And you can play the role of "skeptic" (in management speak) shooting down answers!!
lol, I kid I kid...
seriously itching for the solution now

wtf

ok..i'll explain y my assumption makes sense and y the answer still holds true ...gimme sum tym,i'll type and explain everything,even though it myt take sum time as there are many numbers which comes in the 'not possible list'

gravz84

just do the ones i mentioned..
3,4
13,4
maybe 17, 4 as well

wtf

first of all let us assume that u know the sum and i know the product.
case1:u know your number is 7(4+3),u dont know my number,u say u don't knw the two numbers,i say i dnt knw,then u say u knw and i say even i knw.
now 7=3+4 or 5+2(chuck the '1+something' part in this as well as all future cases as thts out of point) and 12=6*2 or 4*3. when u say tht u know the answer, concluding it from the fact that i dint know the answer initially,u made a mistake at that point because u cant pinpoint the two numbers exactly to be 4 and 3 because u think i have the number 12 with me but i could have even had 10(5*2 or 5+2 for ur case sake)...so if u guess the numbers to b 3 and 4 its just a guess and we cant provide a valid reason for that,which in the end comes out to be some kind of logical fallacy.
similarly for the case 2 and 3.

read the part where i have mentioned the absolute factors thing.for the time being do one thing...make a list of such products(x*y) which cannot have exactly two distinct absolute factors(such that the sum of those factors is less than 100).Now make a list of values of sum(i.e. x+y) that can never be the sum of exactly two absolute factors(call them absolute sum).and try to sort out the relation betwen the sum and the product list.only one pair exist in the list which has exactly one absolute factor and one absolute sum.