



Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Material Type: Exam; Professor: Trotter; Class: Applied Combinatorics; Subject: Mathematics; University: Georgia Institute of Technology-Main Campus; Term: Fall 2003;
Typology: Exams
1 / 7
This page cannot be seen from the preview
Don't miss anything!
Student Name and ID Number MATH 3012 Final Exam, December 8, 2003, WTT
a. How many strings of length 19 have exactly 6 B’s?
b. How many strings of length 19 contain exactly 4 A’s, 2 B’s, 7 D’s and 6 G’s (and no C’s, E’s or F’s)?
c. Of the strings described in part b, how many have all 4 A’s before the 7 D’s?
d. Of the strings described in part c, how many have the 4 A’s and the 7 D’s occuring together as a block of 11 consecutive characters?
b. x 1 + x 2 + x 3 < 59, all xi > 0.
c. x 1 + x 2 + x 3 = 59, all xi ≥ 0.
d. x 1 + x 2 + x 3 ≤ 59, all xi ≥ 0.
e. x 1 + x 2 + x 3 = 59, all xi > 0, x 3 > 12.
Then find integers x and y so that d = 780x + 2772y.
20
8
17
1
5
10
7
15 (^1216)
11
9
2
19
13
14
23
(^3 )
18 21
6
24
25
a. Find a minimum partition of this poset into antichains.
1 2
3 4
5
6
7
8
9
10
1 2 3
4 6
7
5
(^8 )
1
2
3 4
6
7
5
1 2
3
6
5
4
graph.txt Kruskal Prim 3 5 14 4 7 18 5 6 19 3 6 22 1 2 29 2 4 32 1 5 38 2 6 39 3 7 40
p 2 = 5612568098175228233349808831356893505138383383859 489982166463178457733717119362424318136005466967841045532911243455 294271708400354138459486412994014504308676003129248334006892350611 5878221189886491132772739661669044958531131327771
Both p 1 and p 2 are primes. Now consider the number n = p 1 p 2 formed by multiplying them together. Two students, Alice and Bob, are asked to find φ(n), where φ is the Euler φ function. But Alice is given p 1 and p 2 while Bob is just given the value of n. Why does Alice have an unfair advantage over Bob? Does it help Bob to be told that n is in fact the product of two primes—without being told the values of these two primes?