Question

One day a friend visited my house and asked me the ages of my three sons. I replied that the product of my son's ages is 36 and the sum of their ages is equal to my house number. My friend who has a sharp and logical mind, requested me for another hint. I then told him that my eldest son has blue eyes! Following this he quickly told me their ages

Answer 1

Are we supposed the find their ages now? It's not possible from the data given right?

Answer 2

x*y*z=36
x+y+z = #
hmmm

Answer 3

I request another hint too.

Answer 4

no this is logic.. dang it my logic is not working..

Answer 5

There's an eldest son..

Answer 6

So 1*1*36.. that's far too fetched..

Answer 7

36 = 9*4
So the ages could be 9 and 2 and 2

Answer 8

* too far fetched

Answer 9

36=6*3*2

Answer 10

Aren't we supposed to know the house number?

Answer 11

we are supposed to but i think the answer is
6, 3, 2

Answer 12

i dnt knw i got only this info

Answer 13

With this info there are multiple solutions.

Answer 14

A. 1 year, 1 year and 36 years
B. 1 year, 4 years and 9 years
C. 2 years, 2 years and 9 years
D. 3 years, 3 years and 4 years

Answer 15

wait let's see..

Answer 16

36 = 4*9 = 1*1*2*2*3*3

Answer 17

anyone knw y did he give the hint blue eyes?

Answer 18

So there is an eldest son.

Answer 19

sophiya the hint is not blue eyes, the hint is ONE SON IS ELDEST..

Answer 20

yea thomas was right.. hold on i think i got it..

Answer 21

36 = 1*1*2*2*3*3, we need combinations of these:
1+1+(2*2*3*3) = 1+1+36=38 <<impossible

Answer 22

1*1+2+(2*3*3) = 1 + 2 + (2*3*3) = 1 + 2 + 18 = 21 <<possible

Answer 23

Wait, house number have an upper bound?

Answer 24

hmm with this info hw can we get the answer?

Answer 25

Keep doing this:
1*1+3+(2*2*3) = 1+3+12 = 16
1*1+(2*2)+(3*3)= 1+4+9 = 14
1*1+(2*3)+(2*3)= 1+6+6 = 13
2*1+2*1+(3*3) = 2+2+9 = 13
2*1+3*1+(2*3) = 2+3+6 = 11
3*1+3*1+(2*2) = 3+3+4 = 10

Answer 26

Okay there we go those are the possible combinations of the sums.. See we have two of the same sum = 13
so ages are either:
1, 6, 6 or 2,2,9

Answer 27

Now we use the fact that the OLDEST SON has blue eyes. Therefore there's one oldest son, not two.

Answer 28

So we end up with:
2,2,9

Answer 29

2,2,9 are the ages and 13 is the house number

Answer 30

I don't see how it matters that two combinations have the same sum.

Answer 31

atlast shall v end up with 2 2 9?

Answer 32

hey bahroom thank u...

Answer 33

Remember when the friend says that just the product is not enough:
1+1+(2*2*3*3) = 1+1+36=38
1*1+2+(2*3*3) = 1+2+18 = 21
1*1+3+(2*2*3) = 1+3+12 = 16
1*1+(2*2)+(3*3)= 1+4+9 = 14
1*1+(2*3)+(2*3)= 1+6+6 = 13
2*1+2*1+(3*3) = 2+2+9 = 13
2*1+3*1+(2*3) = 2+3+6 = 11
3*1+3*1+(2*2) = 3+3+4 = 10
See the friend is stuck with all these choices and i think the fact that there are two 13s is not a random coincidence..

Answer 34

I was writing this out on paper when i noticed it..haha

Answer 35

I get it. It's not yet possible to get the answer with just these combination. And that only happens when the house number is 13.

Answer 36

i think v cant get answer with this info

Answer 37

http://www.linuxquestions.org/questions/blog/dendron-600233/quick-puzzle-3981/
i got this que frm this link...

Answer 38

hey guys at last anyone got d ans?

Answer 39

hey how can it be 13
ok if there r two combinatios suming up to 13
but then how can we conclude tat it has to be tat

Answer 40

i got it the friend knew the house number but was confused tat dere were two combinations resulting in 13 so he asked for the final clue
i.e. the eldest son. yup tats true fr sure !!!!!

Answer 41

The product of the ages of the three children is 36.
Thus, their possible ages and the sum of their ages are:
1 year, 1 year, 36 years; Sum = 38
1 year, 3 years, 12 years; Sum = 16
1 year, 4 years, 9 years; Sum = 14
1 year, 6 years, 6 years; Sum = 13
2 years, 2 years, 9 years; Sum = 13
2 years, 3 years, 6 years; Sum = 11
3 years, 3 years, 4 years; Sum = 10
In this case, every combination of possible ages has a unique sum of ages - except for two cases, both of which have 13 as the sum. Since the friend could not figure out the ages after looking at the house number, the house number must be 13, because then, the ages could be either 1, 6, 6 or 2, 2, 9. When he was told that the eldest son has blue eyes, he immediately ruled out the set of 1 year, 6 years and 6 years as in this case, the eldest children have the same age. Thus, only one possibility remained, i.e., the ages of the children are 2 years, 2 years and 9 years.