The problem of finding the number of different ways in which a Product of different ordered Factors can
be calculated by pairs (i.e., the number of Binary Bracketings of letters). For example, for
the four Factors , , , and , there are five possibilities: , , ,
, and . The solution was given by Catalan in 1838 as

and is equal to the Catalan Number .

**References**

Dörrie, H. *100 Great Problems of Elementary Mathematics: Their History and Solutions.* New York: Dover, p. 23, 1965.

© 1996-9

1999-05-26