Chapter 5: Q1E (page 370)
Trace Algorithm 1 when it is given n = 5 as input. That is, show all steps used by Algorithm 1 to find 5!, as is done in Example 1 to find 4!.
The value of 5 ! is 120 .
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Prove that 21 divides whenever n is a positive integer.
Suppose that a store offers gift certificates in denominations 25 dollars and 40 dollars. Determine the possible total amounts you can form using these gift certificates. Prove your answer using strong induction.
Give a recursive algorithm for finding the minimum of a finite set of integers, making use of the fact that the maximum of n integers is the smaller of the last integer in the list and the minimum of the first n - 1 integers in the list.
Can you use the well-ordering property to prove the statement: “Every positive integer can be described using no more than fifteen English words”? Assume the words come from a particular dictionary of English. [Hint: Suppose that there are positive integers that cannot be described using no more than fifteen English words. By well ordering, the smallest positive integer that cannot be described using no more than fifteen English words would then exist.]
Prove that the first player has a winning strategy for the game of Chomp, introduced in Example 12 in Section 1.8, if the initial board is two squares wide, that is, a board. [Hint: Use strong induction. The first move of the first player should be to Chomp the cookie in the bottom row at the far right.]
What do you think about this solution?
We value your feedback to improve our textbook solutions.
