Problem:
A cryptographic code is designed as follows. The first time a letter appears in a given message it is replaced by the letter that is place to its right in the alphabet (assuming that the letter is one place to the right of the letter ). The second time this same letter appears in the given message, it is replaced by the letter that is places to the right, the third time it is replaced by the letter that is places to the right, and so on. For example, with this code the word "banana" becomes "cbodqg". What letter will replace the last letter in the message
Answer Choices:
A.
B.
C.
D.
E. \mathrm
Solution:
The last is the th appearance of this letter in the message, so it will be replaced by the letter that is
letters to the right of . Since the alphabet has letters, this letter is coded as .
The problems on this page are the property of the MAA's American Mathematics Competitions