A mother and her friend are talking about how many chidren they have. The friend knows how many daughters the mother has, but doesn't know how many sons she has. The mother says:

"All of my children have the same amount of brothers and the same amount of sisters as the other children."

Now the friend knew how many sons she had. How many sons did the mother have?

let x = number of boys

let n = number of girls

for each girl she has (n - 1) sisters + x brothers

for each boy he has n sisters and (x - 1) brothers

if each boy has the same number of brothers and

sisters as each girl then that means that

(n - 1) girls + x boys = n girls + (x - 1) boys

for there to be an equal number of brothers for

each sibling then x needs to be equal to x - 1

which is not possible.

also for there to be an equal number of sisters

for each sibling then n needs to be equal to n - 1

which also is not possible.

if you had just girls then each sibling would have

n - 1 sisters and 0 brothers, which IS possible.

so the number of sons is 0.

Posted by jaypee on 2003-10-25 13:26:46