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?

zero.

If the mother has b boys and g girls, then each boy would have b-1 brothers and g sisters, while each girl would have g-1 sisters and b brothers.

The only thing that can be deduced from the mother's statement is that her children, if they exist, are either all boys or all girls.

That way, each of b boys would have b-1 brothers and 0 sisters, or each of g girls would have g-1 sisters and 0 brothers.

The final possibility is that there are no boys or girls at all, and the mother's statement (while meaningless) is vacuously true.

Since the friend knew the number of daughters beforehand, but not the number of sons; and she knew the number of sons after, that implies that the mother has some nonzero number of daughters, and the friend realized that she could not have any sons at all.

The answer is zero.

Posted by DJ on 2003-10-25 10:45:50