How old are the 3 girls?

Question

a women announces that she has 3 girls the product of the ages is 72 and the sum is the womens house number. the oldest daughter likes pudding what are the 3 ages and how do you know that thsoe are the 3 ages?

Answer 1

This problem makes assumptions, some of which are valid and some that might not be.

The two sets of ages that contain twins also add up to 14 (3,3,8) and (2,6,6). I have seen versions of this problem when a favorite food for either the youngest or the oldest daughter is mentioned. This is supposed to help determine which of these groups of ages is the correct one.

The problem with the assumption made is that if there were 6 years old twins, one was still born before the other and is the oldest daughter who likes pudding. This does not eliminate either set and it is based upon reality and not a trick.

This problem is supposed to be cute or clever. Perhaps it is only interesting.

Answer 2

You didn't quite phrase it correctly, but here's what I found:

The host at a party turned to a guest and said. " I have three daughters and I will tell you how old they are. the product of their ages is 72. The sum of their ages is my house number. How old is each." The guest rushed to the door, looked at the house number and informed the host that he needed more information. The host then added "The oldest likes pudding." The guest then announce the ages of the three girls.

What are the ages of the three daughters, assuming all ages are whole numbers?

As a product of three numbers, 72 can be written in the following ways with the sums following...

numbers sum
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

other ways of having a product of 72 with three numbers repeat the ways already listed.

When the guest rushed out the door and checked the house number, the house number itself did not provide enough information. Since all the sums appear only once except for 14, the house number must be 14. The next clue was that the oldest likes strawberry pudding implying that there is a single oldest child and not a pair of oldest twins.

So the correct ages would be 3, 3, and 8.

Answer 3

DetroitBr got it exactly right, although it WAS phrased correctly. You don't have to say explicitly that the house # is known, since that is implied by the inclusion of the 'oldest daughter likes pudding' clause. The only purpose of this info is to confirm that one and only one daughter is the oldest. The only way this info can be used is to sort out which of the 2 candidate sequences is the valid one. Each of these sequences (but no other pair) have the same sum, which has to be the house #.

Richard: Lighten UP! STILL BORN? Gimme a break.....! The problem is perplexing enough without throwing in a curve ball like that!

First encountered this one in 1981 under the title 'Strange Distribution' The product was 1296, which made the list of sequences a bit longer than the problem above, but still manageable. This is still one of my all time favorites.

Answer 4

This does not have enough information. The womans house number is needed.
First you find all possible combinations that would lead to a product of 72
72,1,1=74
36,2,1=39
24,3,1=28
18,2,2=22
18,4,1=23
12,3,2=17
12,6,1=19
6,6,2=14
6,3,4=13
I don't know why it would say the oldest daughter likes pudding.

Answer 5

2,3, and 12 because she lives at 17 Blank Avenue and the only people who like pudding are 12 year olds.