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 -length sequences without repetitions of the elements of given set 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 the 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 uand 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 code fragment solving combinatorial puzzle by enumerating and testing all possible configurations