ok let’s start our first Problem as a love story
A man wanted to marry a woman. She agreed to marry him, if and only if he can guess the age of all her 3 daughters. She gave him 2 clues:
1. The product of the age of her daughters is 36
2. The sum of the age of her daughters equals to the address of the house next door
The man made some calculations, went out to find out the address of the house next door, but still could not arrive with the answer. He begged for one more clue. Pitying the man (I think she wanted to marry him too), she gave him one more clue:
3. Her oldest daughter loves strawberry
Instantly, the guy got the answer and they were happily married to each other.
The question: How did he solve it?
henry Said:
on November 1, 2008 at 9:54 am
I think the answer is 9 , 2, 2
The solution can be got by factorizing 36 and getting the sum of factors
so
Factors : sum
36,1,1 : 38
18,2,1 :21
12,3,1:16
9,2,2 : 13
9,4,1:14
6,3,2: 11
4,3,3:10
6,6,1:13
As the man get confused after the two key het must got the answers
9,2,2:13
6,6,1:13
with the 3rd clue the woman told him there is an old daughter so right answer is 9,2,2
AlaaShaker Said:
on November 1, 2008 at 2:40 pm
OK .. So, for the first clue, you have to write down all 3-numbers that multiply to 36 and add them:
> 1 x 1 x 36 – Sum = 39
> 1 × 2 × 18 – Sum = 21
> 1 × 3 × 12 – Sum = 16
> 1 × 4 × 9 – Sum = 14
> 1 × 6 × 6 – Sum = 13 **
> 2 × 2 × 9 – Sum = 13 **
> 2 × 3 × 6 – Sum = 11
> 3 × 3 × 4 – Sum = 10
Now to the second clue .. Since the second clue didn’t help the guy, this means it indicated two possible answers. So, if the address of the house next door is 13, he won’t be able to pick the correct answer, coz there’re two different 3-numbers-set that could lead to 13.
Here comes the last clue, since she mentioned having an “eldest” daughter, then the ages can’t be 1, 6 and 6, coz this way she won’t have an eldest!
The solution is 2, 2, and 9 …
jaqoup Said:
on November 1, 2008 at 6:05 pm
OK till now we have two winners
Alaa Shaker
henry
we had an easy start i think (-_^)
henry Said:
on November 1, 2008 at 7:51 pm
Seems that we badly need to marry
Menna Said:
on November 1, 2008 at 10:52 pm
The daughters age’s are 2,2,9
Menna Tawilla Said:
on November 2, 2008 at 12:34 am
And there is another Winner: Menna Mostafa
I agree with U Abdalla “Jaqoup”, let’s make it harder the next week
jaqoup Said:
on November 2, 2008 at 12:58 am
lool
we have a semi winner here
Menna
she just wrote the final answer while in the problem statement
” The question: How did he solve it? ”
not
” The question: What are the girls ages? ”
she got the right answer without steps …
she seems to be using MATLAB
Metal_ Said:
on November 2, 2008 at 3:12 am
I hate this story telling style.. but what the hell!
The guy makes use of the first clue by listing all possible unique ages’ combinations of which the product is 36, that’s 8 combinations*… now he moves on to the next clue that says, the right combination has the sum of Y ( Next house’s address).
So, all he has to do is lookup the combinations’ list that for a one that yields sum of Y to get married, but too bad for him, two combinations** yields the same exact sum…the same address.. .. 13(that’s why he couldn’t get it right..otherwise, he can’t do arithmetic). He gets the third stupid strawberry clue that implies” My oldest daughter is really really young!!” so he picks up the combination with the smaller largest factor(age)***, that’s all!
*{ {1, 1, 36}, {1, 2, 18},
{1, 3, 12}, {1, 4, 9},
{1, 6, 6}, {2, 2, 9},
{2, 3, 6}, {3, 3, 4}}
** { {1, 6, 6}, {2, 2, 9} }
*** Not sure if got this clue right, but either ways, I made my point.
Roaa Mohammed Said:
on November 2, 2008 at 10:19 am
I didn’t find any rules saying that old ACMers can’t participate, so I decided to answer
well, by getting all the combination that gives a product of 36, we will find that 2 of them have the same summation (that’s why he couldn’t know from the second info)
1*6*6 & 2*2*9
As she mentioned ‘eldest girl’, this makes the second combination wins.. & her girl ages are 2,2 & 9..
Menna Said:
on November 2, 2008 at 10:44 am
I didn’t notice that you wanted explanation as well, sorry
The explanation is:
since the knowing the product didn’t help him in figuring out the ages, that means that there’s more than one combination that may lead to the same product and addition, so by factorizing 36, i found 2 combination that may lead to the same addition which are:
2,2,9
6,6,1
By using the third clue [her eldest] that means no older twins, excluding the second combination, leaving the the 2,2,9 combination
Menna Said:
on November 2, 2008 at 10:49 am
LooooooL
Can MATLAB be useful in this?!!!!!
I like this competition very much, Keep the good work on
jaqoup Said:
on November 2, 2008 at 11:43 am
and another 2 winners
Metal_ (who didn’t like the story
)
)
Roaa Mohammed ( an old ACMer
we have a nice number of smarties here
ZooM Said:
on November 2, 2008 at 1:55 pm
Well, here are all the possibilities….
(36,1,1) > Sum = 38
(18,2,1) > Sum = 21
(12,3,1) > Sum = 16
(9,4,1) > Sum = 14
(6,6,1) > Sum = 13 << Sum = 13 << Sum = 11
(4,3,3) > Sum = 10
Since the man got the number of house next door, it makes no sense if he didn’t find the answer by now. so there must be two identical sums. (6,6,1) and (9,2,2).
And since she said she has an OLDEST daughter, then the first answer is wrong and the second answer is correct.
(9,2,2)
ZooM
ZooM Said:
on November 2, 2008 at 1:58 pm
Sorry about my previous (wrong) comment.
Here is the right one since i don’t want to post it wrong
Well, here are all the possibilities….
(36,1,1) > Sum = 38
(18,2,1) > Sum = 21
(12,3,1) > Sum = 16
(9,4,1) > Sum = 14
(6,6,1) > Sum = 13 << Sum = 13 << Sum = 11
(4,3,3) > Sum = 10
Since the man got the number of house next door, it makes no sense if he didn’t find the answer by now. so there must be two identical sums. (6,6,1) and (9,2,2) .
And since she said she had an ELDEST daughter, then the first is wrong and the second is correct.
(9,2,2)
ZooM Said:
on November 2, 2008 at 2:02 pm
lol, the wp script keeps shortening my comment. here is the right one in a text file….
http://rapidshare.com/files/159912015/acm.txt
Mohamed Hesham Said:
on November 2, 2008 at 4:07 pm
can a kid with 3 or 4 years eats strawbery??
jaqoup Said:
on November 2, 2008 at 4:14 pm
Mohamed Gamal Said:
on November 2, 2008 at 5:16 pm
2,3and 6
jaqoup Said:
on November 2, 2008 at 6:27 pm
we have another winner
of course not Mohamed Gamal
“The right answers will be moderated”
the Winner is ZooM
Ahmad Farid Said:
on November 2, 2008 at 7:35 pm
2, 2, 9
As 1, 6, 6 gives the same sum which is 13 thus he needed another clue which made the first one correct as it has only one oldest daughter.
hafez Said:
on November 2, 2008 at 7:48 pm
Answer
2,,3 & 6
jaqoup Said:
on November 2, 2008 at 7:51 pm
To Ahmad Farid : Yes
To Hafez : nope
AlaaShaker Said:
on November 2, 2008 at 10:29 pm
To Jaqoup and Henry: Yeah, badly .. so I suggest tedoony el gayza naqdan aw besheekat :huh
Mohammed Saudi Said:
on November 2, 2008 at 10:52 pm
My answer is :d,
after calculating the probabilities of the ages , she should immediately know the ages when seeing the address , but this didn’t happened.
so some combinations have the same final summation result which make him confused . 2,2,9 and 6,6,1
the third clue tells the oldest girl loves strawberry .. this leads to the 2,2,9 combination .
Asmaa Magdi Said:
on November 2, 2008 at 11:20 pm
LoL, ana lessa shayfa el so2al da somewhere we shoft egabto kaman
. lw 2olt el egaba bel steps mesh ha7′od 7aga 
fa hastanna b2a lel marra elly gaya inshaAllah 
Omar Mohammad Othman Said:
on November 3, 2008 at 12:08 am
Having the clue that the man didn’t succeed to know the ages from the address house means that he had a conflict. This renders us directly to the only two conflicting triplets: 9, 2, 2 and 6, 6, 1. The last clue states that the eldest girl bla bla bla… I don’t care. “The eldest” is what I do care about, and the answer clearly becomes 9, 2, 2.
Joseph Daniel Said:
on November 3, 2008 at 12:15 am
The children’s ages are 9, 2 , 2 .
Jaqoup Said:
on November 3, 2008 at 7:33 am
To AlaaShaker : “what gayza?”
and another three winners
Mohammed Saudi
Omar Mohammad Othman
Joseph Daniel (semi winner) he didn’t answer the question.. just the ages
ok who’s next ?
Fourat Adel Said:
on November 3, 2008 at 8:57 am
2,2,9
as the story mentioned that the man couldn’t find the answer
knowing the address of the next door
x+y+z=w
knowing (w) didn’t help him .
After getting the factors of 36
the only option for w is 14
and so x,y,z could be
1,6,6
or
2,2,9
and so the man got confused
when she told him that her oldest girl loves so and so
he became sure that the ages are 2,2,9
Ahmad Hosny Said:
on November 3, 2008 at 9:47 am
if we did numerical analysis to all factors of number 36 and get the summation of these factors we will find only 2 pairs with the same sum (2,2,9) & (1,6,6) from the third clue she has only one oldest daughter ! so the answer is (2,2,9 ) .
5olio Said:
on November 3, 2008 at 11:04 am
ممكن 2 2 9
لان اكيد بنت عندها سنتين مش هتبقى بتحب الفراولة
هو مش strawberry
معناها فراولة ولا انا بيتهيألى ؟؟
profahmedsaad Said:
on November 3, 2008 at 12:38 pm
It’s 2,2,9
as when he got only the first two clues, he got confused between the 2 only summation similar solutions ( 2,2,9 && 1,6,6 ) -> which is 13.
so after knowing that the oldest, which means that the oldest is only one , not twins
so the second solution (1,6,6) is rejected, so the solution is (2,2,9)
Omar Mohammad Othman Said:
on November 3, 2008 at 1:02 pm
Will these nice problems be published every 7 days exactly? I want to be informed regularly, otherwise I may forget…
Amr Attia Said:
on November 3, 2008 at 1:03 pm
That idea is really nice but Let it Be 2 problems a week please.
2 , 2 , 9
Jaqoup Said:
on November 3, 2008 at 1:49 pm
To Omar Mohammad Othman: isA a problem will be posted every Saturday 12:00 am (Automatically scheduled)
To Amr Attia: we’ll try isA
The Question is “HOW did he solve it?”
To * :
Pliz let the problem thread be for the solutions only
and for any other comments u r extreeeemly welcome but in the fixed main thread at the blog’s home page
Jaqoup Said:
on November 3, 2008 at 2:53 pm
New Winners:
Fourat Adel
)
Ahmad Hosny ( numerical analysis
profahmedsaad
Mohamed Gamal Said:
on November 3, 2008 at 5:22 pm
9 , 4 & 1 Ya Rab b2a
Mona Yehia Said:
on November 3, 2008 at 5:36 pm
4 3 3
Jaqoup Said:
on November 3, 2008 at 6:03 pm
To * :The Question is “HOW did he solve it?”
The ages are part of the solution not the solution
Mona Yehia Said:
on November 3, 2008 at 6:23 pm
since the man tried to look for the address and didn’t arrive with the answer..it means there was a conflict and if we listed the possible ages and their sums..the only conflict will be between 6 6 1 & 9 2 2, since she said that the oldest daughter loves strawberry..it means that there is only one old daughter..they are not twins so 6 6 1 is not possible…
so the answer should be 9 2 2
Mohamed Gamal Said:
on November 3, 2008 at 6:29 pm
since the man didn’t arrive with answer with help off the address of the door ,it means that theres 2 cases or mor that the sum of the ages are equal . so the possibles may be 6,6&1 or 9 ,2&2. the third key solve this problem as the saied her oldest daughter that meens that 6,6&1 is n’t possible so it should be 9,2&2 . :d we Ya Rab b2a
Jaqoup Said:
on November 3, 2008 at 6:34 pm
To Mona Yehia & Mohamed Gamal: Yes
Joseph Daniel Said:
on November 3, 2008 at 7:41 pm
Ok, here’s how I reached it
He wouldn’t have needed another clue if the answer was 2,3,6(11) or 3,3,4(10)
The number of the house next door should have been 13 so he wanted to know if it is 9,2,2 or 6,6,1
Since there is an oldest then it’s 9,2,2 not 6,6,1
Hope that’s it.
aya yehia Said:
on November 3, 2008 at 10:49 pm
eah dah how amomken gaz a7al ezya??
Jaqoup Said:
on November 3, 2008 at 11:58 pm
To aya yehia: ok i’m in SC but my ability to understand what u mean by this phrase is limitd
na3am
Amr Attia Said:
on November 4, 2008 at 1:35 am
When u notice the sums of all 3 numbers having product equals 36, u will find that only 2 sums are having the sum 13, which caused the conflict to our guy, the 2 sums are:
1 * 6 * 6
2 * 2 * 9
when that smart woman said that her oldest daughter loves whatever, that meant that there is only one old daughter, so the correct ages would be 2,2,9.
Regards.
Mona Yehia Said:
on November 4, 2008 at 1:40 am
i think she means : hwa momken kaza answer ezay ??
MMH Said:
on November 4, 2008 at 6:34 am
How did he solve it?
Depending on given info’s
1- the man went out to find out the next door house number and still can’t decide, that means that he found the next door house number will not give him only one combination
2- the 3rd clue tell us that there is one daughter oldest the others
so
getting there ages product primes will give us 2 2 3 3 and will have
2 2 9
2 3 6
3 3 4
and will add
1 6 6
now we have
2+2+9 = 13 and 1+6+6 = 13
and the product of each combination is 36
using the 3rd clue it can’t be 1 6 6 (there is 2 oldest daughters)
so 2 2 9 it perfect answer
Ahmad Fathi ElRuby Abd ElWahab Said:
on November 5, 2008 at 5:26 pm
the answer is 2,2,9
because when the man go to the next house will find it 13
(if the man found the address of the next house not=13)
he will find the result with no help
then when he know that there is an oldest daughter
then 1 6 6 won’t be the true answer
then the true answer is 2,2,9
Amr Saqr Said:
on November 5, 2008 at 7:45 pm
boss ya 3am jaqoup
ha2ollak el 7all elle ana already 2oltholak aslan
bas 3ashan ab2a winner :@:@:@:@
awel 7aga howwa akeed gamb el combinations kollaha bta3et el 3 arqam elle nedrabhom f ba3d w yeddena 36
welle homma
1 6 6 sum = 13 <—
1 2 18 sum = 21
1 3 12 sum = 16
1 4 9 sum = 14
2 2 9 sum = 13 <—
2 3 6 sum = 11
3 3 4 sum = 10
feeh 7alleen bas magmo3hom nafs el 7aga welle howwa 13
, feeh 2 oldest daughters 
:D:D
fa heya de akeed el 7aga elle la5bateto akeed lamma ra7 shaf el address w ma3refsh
el mohem ya3ne 2enn lamma el bett 2aletlo her oldest daughter
fa 3alatool 2am 2ayel el 7all elle howwa 2 2 9
la2enn da feeh oldest daughter 2ennama 1 6 6 mafehoosh oldest daughter
bas keda, w 2eb2o hato masa2el sa3ba ba2a
Jaqoup Said:
on November 5, 2008 at 7:47 pm
Some Other Winners
Joseph Daniel
Amr Attia
MMH
Ahmad Fathi ElRuby Abd ElWahab
Amr Saqr
People are getting smarter by time
Marwan Ezz Said:
on November 6, 2008 at 4:58 am
1) We analyse the number 36 to get its factors : 2, 2, 3, 3, 1
2) next, from those factors, we obtain all the combinations that give the number 36 as a product of three numbers and calculate the sum of the numbers that form each combination
the combinations will be as follows:
{2, 18, 1} and their sum = 21
{2, 6, 3} and their sum = 11
{2, 9, 2} and their sum = 13
{3, 3, 4} and their sum = 10
{1, 6, 6} and their sum = 13
{1, 9, 4} and their sum = 14
{3, 12, 1} and their sum = 16
3) From the previous combinations we note that the two combinations {2, 9, 2} and {1, 6, 6} give the same sum (13) and this explain why the second clue wasn’t enough to solve the problem .
In other words, if the address of the house next door was any of the combinations except these two, then the man should be able to conclude the answer immediately.However , the man couldn’t find the answer according to the second clue and this means that the address of the house must be 13 and though the man was faced with 2 possibilities for the ages of the three girls:{2, 9, 2} and {1, 6, 6}
4) If we look closer at the third clue (Her oldest daughter loves strawberry) we would conclude that there is one oldest daughter which unqualifies one of the two possibilities, namely {1, 6, 6}, because this combination indicates that there is two oldest girls .Thus, the man instantly found that the correct answer must be {2,9,2}
Women’s Love [Answered] « acmASCIS Weblog Said:
on November 7, 2008 at 12:00 am
[...] U can go check the solution here [...]