Brain Teasers
Daughters and Sons
A mother and her friend are talking about how many children 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?
"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?
Hint
We don't have to know the number of daughters - all that's needed is the mother's statement, and the fact that the friend knows the number of daughters.Answer
The mother says that her children all have the same amount of brothers and same amount of sisters as each other. If B is the number of sons and G the number of daughters, then each boy has B-1 brothers and G sisters, and each girl has G-1 sisters and B brothers.For any combination of brothers and sisters to fit into that rule, there must be either no sons or no daughters, because if there were some of each the sons would have more sisters than the daughters, and vice versa.
If the friend knows the mother has no daughters, the statement does not help her know how many sons there are, as there could be any number.
The friend knows the value of G, and if it was any number other than 0 (which it definitely is), the number of sons would have to be 0.
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