On each homework assignment, please write (i) your name, (ii) name of course, and (iii) homework number. You are allowed and encouraged to work together on homework. Yet, each student is expected to turn in their own work. In general, late homework will not be accepted. However, you are allowed to turn in **up to three late homework assignments with no questions asked**. Unless you have made arrangements in advance with me, homework turned in after class will be considered late. When doing your homework, I encourage you to consult the Elements of Style for Proofs as a reference.

The following assignments are to be turned in at the end of the indicated class period. I reserve the right to modify the assignment if the need arises. These exercises will form the basis of the student-led sharing of solutions/proofs each day. Homework assignments will be graded on a $\checkmark$-system. During class, **you are only allowed to annotate your homework using the colored marker pens that I provide**.

**Homework 1:**Read the syllabus and write down 5 important items.*Note:*All of the exam dates only count as a single item. Turn in on your own paper at the beginning of class. (Due Friday, January 20)**Homework 2:**Stop by my office (AMB 176) and say hello. If I'm not there, just slide a note under my door saying you stopped by. (Due by 4PM on Friday, January 20)**Homework 3:**Complete Problems 1-4 from the Problem Collection. (Due Friday, January 20)**Homework 4:**Complete Problems 5-8 from the Problem Collection. (Due Monday, January 23)**Homework 5:**Complete Problems 9-11 from the Problem Collection. (Due Wednesday, January 25)**Homework 6:**Complete Problems 12-14 from the Problem Collection In addition, revisit Problem 7 and attempt to justify why the answer cannot be 10 or larger. (Due Friday, January 27)**Homework 7:**Complete Problems 15-17 from the Problem Collection. (Due Monday, January 30)**Homework 8:**Complete Problems 18-20 from the Problem Collection. (Due Friday, February 3)**Homework 9:**Revisit Problem 20 and find a way to find fastest 3 horses in 7 races and then find a convincing argument that you can't do it in 5 or 6 races. Also, verify that Michael's proposed solution to the problem involving $x-y=85$ and $\sqrt{x}+\sqrt{y}=17$ that was encountered on Friday last week is unique or find the rest of the solutions. Lastly, complete Problem 21 from the Problem Collection. (Due Wednesday, February 8)**Homework 10:**Complete Problems 22-24 from the Problem Collection. (Due Friday, February 10)**Homework 11:**Complete Problems 25-28 from the Problem Collection. (Due Monday, February 13)**Homework 12:**Complete Problems 33-35 from the Problem Collection. Also, attempt to verify that 17 minutes is the minimum in Problem 26. (Due Friday, February 17)**Homework 13:**Revisit Problem 35 and then complete Problems 36 and 37 from the Problem Collection. For Problem 36, try to sort out whether we can determine the counterfeit coin in at most 3 weighings when we have 1 through 11 coins. (Due Monday, February 20)**Homework 14:**Complete Problems 38-40 from the Problem Collection. (Due Wednesday, February 22)**Homework 15:**Complete Problems 41-43 from the Problem Collection. (Due Monday, February 27)**Homework 16:**If necessary, revisit Problems 42 and 43. Also, complete Problems 44-46 from the Problem Collection. (Due Wednesday, March 1)**Homework 17:**Keep working on Problems 42 ($n=9$ case), 45, and 46. In addition, complete Problem 47 from the Problem Collection. (Due Friday, March 3)**Homework 18:**Complete Problems 48-50 (Magic!, Two Deep, Checker Mate) from the Problem Collection. (Due Monday, March 6)**Homework 19:**Complete Problems 51-53 (The Good Teacher, One Overs, Quilt) from the Problem Collection. (Due Wednesday, March 8)**Homework 20:**Complete Problems 54-55 from the Problem Collection. (Due Monday, March 20)**Homework 21:**Complete Problems 56-57 from the Problem Collection. (Due Wednesday, March 22)**Homework 22:**Complete Problem 58 from the Problem Collection. (Due Friday, March 24)**Homework 23:**Complete Problems 59-61 from the Problem Collection. (Due Monday, March 27)**Homework 24:**Complete Problems 62-64 from the Problem Collection. (Due Friday, March 31)**Homework 25:**Keep working on Problems 63 and 64 and then complete Problem 65 from the Problem Collection. (Due Monday, April 3)**Homework 26:**Keep working on Problem 64 and complete Problems 66-67 from the Problem Collection. For Problem 64, what remains to be justified is that if $A$ adn $B$ are adjacent enemies, then you can always find an adjacent pair $C$ and $D$ such that $A$ and $C$ are no enemies and $B$ and $D$ are not enemies. (Due Wednesday, April 5)**Homework 27:**Complete Problems 68-70 from the Problem Collection. (Due Friday, April 7)**Homework 28:**Complete Problems 71-72 from the Problem Collection. (Due Monday, April 10)**Homework 29:**Complete Problems 73-75 from the Problem Collection. (Due Friday, April 14)**Homework 30:**Complete Problems 76 and 77 from the Problem Collection. (Due Monday, April 17)**Homework 31:**Complete Problems 78-80 from the Problem Collection. (Due Wednesday, April 19)**Homework 32:**Continue working on Problem 80 and complete Problem 81 from the Problem Collection. (Due Friday, April 21)**Homework 33:**Complete Problems 82 and 83 from the Problem Collection. (Due Monday, April 24)**Homework 34:**Complete Problems 84-86 from the Problem Collection. (Due Friday, April 28)**Homework 35:**Continue working on Problem 84 and complete Problems 87 and 88 from the Problem Collection. (Due Monday, May 1)**Homework 36:**Complete Problems 89-91 from the Problem Collection. (Due Wednesday, May 3)**Homework 37:**Complete 3 from among Problems 92-95 from the Problem Collection. (Due Friday, May 5)

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MAT 226: Discrete Math

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Flagstaff and NAU sit at the base of the San Francisco Peaks, on homelands sacred to Native Americans throughout the region. The Peaks, which includes Humphreys Peak (12,633 feet), the highest point in Arizona, have religious significance to several Native American tribes. In particular, the Peaks form the Diné (Navajo) sacred mountain of the west, called Dook'o'oosłííd, which means "the summit that never melts". The Hopi name for the Peaks is Nuva'tukya'ovi, which translates to "place-of-snow-on-the-very-top". The land in the area surrounding Flagstaff is the ancestral homeland of the Hopi, Ndee/Nnēē (Western Apache), Yavapai, A:shiwi (Zuni Pueblo), and Diné (Navajo). We honor their past, present, and future generations, who have lived here for millennia and will forever call this place home.