These are the best and most fun math riddles you can find. All of these tricky riddles are based on real math concepts and can be solved with purely math and logic.
These are the best and most fun math riddles you can find. All of these tricky riddles are based on real math concepts and can be solved with purely math and logic.
The one that I find interesting: Mr. Smith has two children. If the older child is a boy, what are the odds the other child is also a boy?
Assuming that any given child is a boy or a girl are equally likely, there are four equally likely cases for two children:
Boy, Boy
Boy, Girl
Girl, Boy
Girl, Girl
where the first child listed is the older.
"The older child is boy" reduces this to
Boy, Boy
Boy, Girl
The other child is also a boy happens exactly once in these two equally likely cases so the probability of the other child also being a boy is 0.5. However, strictly speaking, the "odds" that the second child is also a boy are "one to one".
Consider this simple variation: "Mr. Smith has two children. If one of the children is a boy, what is the probability the other child is also a boy?"
Again, the four equally likely possibilities ate
Boy, Boy
Boy, Girl
Girl, Boy
Girl, Girl
But now the fact that "one of the children is a boy" reduces this to three equally likely cases:
Boy, Boy
Boy, Girl
Girl, Boy
and the other child is a boy in only one of the three cases. Given that one of the children is a boy, the probability that the other child is also a boy is 1/3. (And the odds that the other child is also a boy is "one to two".)
Notice that in the first question we were told that "the older child is a boy" but in the second question we were told that "one of the children is a boy". We are given less information in the second than in the first.