Problem Name

Problem Description

Notes

discrete_math_1

Define what it means for an integer to be square. For example, the integers 0, 1, 4, 9, and 16 are square. Your definition should begin: An integer x is call ‘square’ provided….

discrete_math_2

Prove that the product of an even integer and an odd integer is even.

discrete_math_3

Evaluate without calculating 100! or 98!.

discrete_math_4

One hundred people are to be divided into ten discussion groups with ten people in each group. In how many ways can this be done?

discrete_math_5

A special type of door lock has a panel with five buttons labeled with the digits 1 through 5. This lock is opened by a sequence of three actions. Each action consists of either pressing one of the buttons or pressing a pair of them simultaneously. For example, 12-4-3 is a possible sequence. The sequence 12-4-3 is the same as 21-4-3 because the 12 or the 21 simply means to press buttons 1 and 2 simultaneously.
(a) How many different sequences are possible?
(b) How many different sequences are possible if no digit (or pair of digits) is repeated in the sequence?