# Amar, Akbar and Anthony

Question: "We - Amar, Akbar and Anthony - each have some children.
1. Amar has at least one girl and twice as many boys as girls.
2. Akbar has at least one girl and three times as many boys as girls.
3. Anthony has at least one girl and three more boys than girls.
4. When I tell you the number of children we have altogether - a number less than 25 - you will know how many children I have, but not how many children each of others has."
Who is the speaker and how many children he have?

Amar is the speaker and he have 6 children.
Find out possible number of children each can have and then use trial-n-error.
From (1), Amar has at least 3 children and any number from -
3, 6, 9, 12, 15, 18, .....
From (2), Akbar has at least 4 children and any number from -
4, 8, 12, 16, 20, 24, .....
From (3), Anthony has at least 5 children and any number from -
5, 7, 9, 11, 13, 15, 17, 19, 21, .....

From (4), total number of children are at most 24. Also, if total number of children is  odd, Amar must have an even number of children and if total number of children is even,
Amar must have an odd number of children.
Using some trial-n-error:
* The total number of children can not be 13 as no three numbers - one from each sequence - can add up to 13.
* The total number of children can not be 12, 14, 15, 16 or 17 as there is just a one way to get that sum by adding up one number from each sequence. Hence, we will know how many children they individually have. Thus, contradicts the statement (4).
* The total number of children can not be 18, 20, 21, 22, 23 or 24 as there are multiple ways to get that sum. Hence, we won't know how many children, at least one of them have. Again contradicting the statement (4).
Thus, the total number of children must be 19 and there are two possible cases:
1> Amar-6, Akbar-4, Anthony-9
2> Amar-6, Akbar-8, Anthony-5

In both the cases, we know that Amar have 6 children and hence Amar is the speaker.