Challenge #12

Parenthesizations

Imagine that we have five pairs of parentheses, meaning five ( symbols and five ) symbols.

How many ways can we write these ten symbols to create a “valid” arrangement of parentheses?

For example: If we have only two pairs of parentheses, we can write valid parenthesizations: ()() and (( )). On the other hand, the arrangements ())( and )()( are not valid.

Follow-up Challenges

A group of 10 people are seated around a circular table. How many ways can these people simultaneously shake hands such that none of the handshakes cross each other?

For example: If there were 6 people at the circular table, the image on the left is a valid way the people could shake hands. The image on the right is an invalid configuration (two handshakes cross.)

Response Videos

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