A tricky math riddle?

Question

Two old college friends bump into each other one day at Stafford Street. They hadn't seen each other in over 20 years.
The first guy says to the second: "how have you been?"
Second: "Great! I got married and I have three daughters now"
First: "Really? how old are they?"
Second: "Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there.."
First: "Right...ummm...oh wait, I still don't know"
second: "Oh sorry, the oldest one just started playing the piano"
First: "Wonderful! my oldest is the same age!"

QUESTION: How old are the daughters?

Answer 1

3,3,8

The reason is that if you write down all possible three integers whose product become 72 you reach following sets, whose sum are written also:
1,1,72 => 74
1,2,36 => 39
1,3,24 => 28
1,4,18 => 23
1,6,12 => 19
1,8,9 => 18
2,2,18 => 22
2,3,12 => 17
2,4,9 => 15
2,6,6 => 14
3,3,8 => 14
3,4,6 => 13

The reason that the second friend was unable firstly to figure out the values is that the number of building was 14 (since all other summations are unique, therefore he then could easily find out) and the additional explanation of the first friend made him sure that there are no twins in elder age (so the oldest was meaningless). Therefore, we can judge that they should be a twin at 3 and the oldest at 8.

Answer 2

72 = 2*2*2*3*3

Possible ages: 1, 2, 3, 4, 6, 8, 9, 12, 18 (not 24, 36, 72 since they knew each other 20 years ago)

Possible combinations and their sums:

18, 4, 1 = 23
18, 2, 2 = 22
12, 6, 1 = 19
12, 3, 2 = 17
9, 8, 1 = 18
9, 4, 2 = 15
8, 3, 3 = 14
6, 6, 2 = 14
6, 4, 3 = 13

Of these, only two combinations have the same sum (which is a characteristic of the correct answer, since that information did not solve the problem). Remaining possible combinations:

8, 3, 3
6, 6, 2

Only the first combination has an OLDER daughter (as opposed to older twins), so the daughters' ages are 8, 3, and 3.

Answer 3

3, 3, 8


After looking at the building number the man still can't figure out what their ages are (we're assuming since he's an college grad, he can factor 72 and add up the sums), so the building number must be 14, since that is the only sum that has more than one possibility.

finally the man discovers that there is an oldest daughter. that rules out the "2 6 6" possibility since the two oldest would be twins. therefore, the daughters ages must be "3 3 8".


Although, it is possible for two siblings to have the same age but not be twins, for instance one is born in january, and the next is conceived right away and delivered in october. next october both siblings will be one year old.

Answer 4

When he said that the sum is the same as the number of a building, and the other said he still doesn't know, that means there are 2 or 3 or ... sets of numbers with a product of 72 and the same sum. Listing all 3 factors of 72, you notice that only two sets have the same sum, 14. they are
6 6 2 and
3 3 8

The clue is there is only one oldest, so 6 6 2 is not applicable because the eldest are twins.

The answer is 3,3 and 8.

^_^

Answer 5

24

Answer 6

2, 4 and 9

Answer 7

The three daughters are 2 years, 6 years and 6 years old.

Answer 8

3,3, and 8

You know this because the there must have been more than one possibilities of ages when the man couldn't solve it from looking at the house number (which we don't know) and because there is an oldest child (which leaves the possibility of twins)

3*3*8= 72

Answer 9

24 years

Answer 10

the twins are 3 and the oldest is 8