Two mathemmaticians Mr. Pascal and Mr euler are walking down the steet. Here is a portion of their conversatio

Question

Pascal: How many children do you have?
Euler: Three
Pascal: How old are they?
Euler: The product of their ages is 36
Pascal: That doesn't help me
Euler: The sum of their ages is the same as the house number on that house across the street.
Pascal: It's still impossible for me to tell their ages
Euler: My eldest loves chocoalte cake.
Pascal: Aha! Now I know how old they are.

How did Pascal know? How old are Euler's children? what is the number of the house?

Answer 1

9, 2 and 2.

There are several possible factorisations of 36:
6-6-1 9-2-2 (both add to 13).

The remaining factorisations all have different sums from one another (and from 13).

9-4-1
12-3-1
4-3-3
6-3-2
18-2-1
36-1-1

From the fact that the house number (13) does not point to a unique solution we deduce that the answer must be either 6-6-1 or 9-2-2. and we eliminate the other solutuons

From the fact he has an eldest child we can eliminate 6-6-1 and that leaves us with 9-2-2 as the answer

Answer 2

36 = 1* 2 * 2 * 3 * 3 * 36

possible ages:
1, 1, 36 - sum = 38
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

The house number is 13 since any other number would tell him exactly how old the kids are.
When we find out Euler has an eldest, we know their ages aren't 1, 6 and 6. Therefore their ages are 2, 2 and 9

Answer 3

3 possibilities
4 3 3
6 3 2 i think its this 1 because other 2 have 2 same age
9 2 2

hows chocolate cake have anything to do with it?

Answer 4

could also be 1, 3 & 12...

still thinking about the house # and chocalate cake thing...

Answer 5

that's a good one, touche