HW 1: due Friday 8/27

READ: Chapter 1 and 2.1, p.1-14

BOOK PROBLEMS: None this week.

OTHER PROBLEMS:
A. Decrypt the shift-encrypted message VO DOHA H ILHBAPMBS TVYUPUN.

B. Encrypt ``dog has fleas'' by a one-time-pad 'antedeluvian'.

C. Let a be the number for the month you were born and let b be the number for the day you were born. Find the smallest positive number c that can be written as c=ax+by where x and y are integers (whole numbers). For example, for my birthday March third the equation is c=3x+3y. The smallest positive value is c=3 which happens when x=2 and y=-1 and for many other choices of x and y.

D. The US postal service uses address bar codes on the mail. Each bar code represents 12 digits: the 5 + 4 digits of the zip code, the last 2 digits of the street address, and 1 check digit which is chosen so that the sum of all 12 numbers is divisible by 10. If a machine scans the barcode and finds 12 numbers that do not add up to a multiple of 10, it knows that an error has occurred and will rescan.
i) What is the check digit x for the math department 80523-1874-01-x?
ii) Is it possible that the machine will not notice that it has scanned the barcode incorrectly?