multiple recursion generalizing from binary recursionwe define multiple recursion as process in which function may make more than two recursive calls our recursion for analyzing the disk space usage of file system (see section is an example of multiple recursionbecause the number of recursive calls made during one invocation was equal to the number of entries within given directory of the file system another common application of multiple recursion is when we want to enumerate various configurations in order to solve combinatorial puzzle for examplethe following are all instances of what are known as summation puzzlespot pan bib dog cat pig boy girl baby to solve such puzzlewe need to assign unique digit (that is to each letter in the equationin order to make the equation true typicallywe solve such puzzle by using our human observations of the particular puzzle we are trying to solve to eliminate configurations (that ispossible partial assignments of digits to lettersuntil we can work though the feasible configurations lefttesting for the correctness of each one if the number of possible configurations is not too largehoweverwe can use computer to simply enumerate all the possibilities and test each onewithout employing any human observations in additionsuch an algorithm can use multiple recursion to work through the configurations in systematic way we show pseudocode for such an algorithm in code fragment to keep the description general enough to be used with other puzzlesthe algorithm enumerates and tests all klength sequences without repetitions of the elements of given universe we build the sequences of elements by the following steps recursively generating the sequences of elements appending to each such sequence an element not already contained in it throughout the execution of the algorithmwe use set to keep track of the elements not contained in the current sequenceso that an element has not been used yet if and only if is in another way to look at the algorithm of code fragment is that it enumerates every possible size- ordered subset of and tests each subset for being possible solution to our puzzle for summation puzzlesu { and each position in the sequence corresponds to given letter for examplethe first position could stand for bthe second for othe third for yand so on