# Discrete Math 221

**Question description**

**Answer discussion questions (DQ) with 200-300 words of original work per each question:****DQ1:** Using a search engine of your choice, look up the term *one-way function*. This concept arises in cryptography. Explain this concept in your own words, using the terms learned in Ch. 5 regarding functions and their inverses. Please do not use Wikipedia as a source for your answer.

**DQ2: **Describe a favorite recreational activity in terms of its iterative components, such as solving a crossword or Sudoku puzzle or playing a game of chess or backgammon. Also, enumerate any recursive elements that occur.Describe a favorite recreational activity in terms of its iterative components, such as solving a crossword or Sudoku puzzle or playing a game of chess or backgammon. Also, enumerate any recursive elements that occur.

**DQ3: **While I was looking for interesting DQ possibilities for this week's discussion, I typed the word "recursion" into Google's search engine. The results made me laugh. Try it yourself and explain why it is funny, and then find or come up with a joke relating to this week's learning objectives.

**DQ4: **First, define recursion. Then, describe a situation in your professional or personal life when recursion, or at least the principle of recursion, played a role in accomplishing a task, such as a large chore that could be decomposed into smaller chunks that were easier to handle separately, but still had the semblance of the overall task. Did you track the completion of this task in any way to ensure that no pieces were left undone, much like an algorithm keeps placeholders to trace a way back from a recursive trajectory? If so, how did you do it? If not, why did you not?

**DQ5:** A common result in the analysis of sorting algorithms is that for *n* elements, the best average-case behavior of any sort algorithm—based solely on comparisons—is *O*(*n* log *n*). How might a sort algorithm beat this average-case behavior based on additional prior knowledge of the data elements? What sort of speed-up might you anticipate for such an algorithm? In other words, does it suddenly become *O*(*n*), *O*(*n*log *n*) or something similar?

**Solve the following problems in words if possible:**

**Problem 1: **For the four-digit integers (from 1000 to 9999), how many are palindromes and what are their sums?

**Problem 2:** An executive buys $2490 worth of presents for the children of her employees. For each girl she gets an art kit costing $33; each boy receives a set of tools costing $29. How many presents of each type did she buy?

**Problem 3: **The change machine at Cheryll’s laundromat contains n quarters, 2n nickels, and 4n dimes, where n ∈ Z+. Find all values of n so that these coins total k dollars, where k ∈ Z+.

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