Homework #1 - Due Thursday, January 25th, 2018 - Submitted according to the TA's guidelines.

SECTION        PROBLEM(S)

1.2 #16, 26, 28, 32
1.3                      #12, 14,16, 30, 32
1.4                       #4, 6, 10, 16

Extra Problems:

Problem 1: What is the value of k after the following pseudocode has been executed?
                 k := 0
                for i1 := 1 to n1
                   k := k + 1
                for i2 := 1 to n2
                   k := k + 1
                ...
                for im := 1 to nm
                   k := k + 1

Problem 2: Look up Vandermonde's Identity and prove it combinatorially.

Problem 3: In a version of the computer language, BASIC, the name of a variable is a string of one or two alphanumeric characters, where uppercase and lowercase letters are not distniguished. Moreover, a variable name must begin with a letter and must be different from the five strings of two characters that are reserved for programming use. How many different variable names are there in this version of BASIC?

PLEASE SHOW ALL WORK LEGIBLY IN ALL PROBLEMS.