2017 UNCO Math Contest II Problems/Problem 5

Problem

Double Encryption

(a) Find a substitution code on the seven letters A, B, C, D, E, F, and G that has the property that if you apply it twice in a row (that is, encrypt the encryption), the message ABCDEFG becomes ECBFAGD. Describe your answer by giving the message that results when encryption is applied once to the message ABCDEFG.

(b) Find another such code, if there is one.

Solution

(a) BEAGCDF

(b) CAEGBDF