What is the check digit for the bank routing number 09100001?
(7*0)+(3*9)+(9*1)+(7*0)+(3*0)+(9*0)+(7*0)+(3*1) = 27+9+3 = 39
Note the weights are 7, 3, and 9
So the check digit is 9 (the last digit of the sum)
100
What is the difference between the Caesar cipher and the Vigenere Cipher?
Caesar cipher: encodes by "shifting" the letter three places (i.e. A --> D)
Vigenere cipher: encodes by adding the letter positions of the message and the code word together, finds the new letter by mod 26 (example to follow)
100
What is the length of this genome sequence?:
AATCGATC
8 (it really is that easy)
100
Given 55, 89, 144, in the Fibonacci Sequence, what is the next term?
89 + 144 = 233
100
What are the characteristics of a SEMI-REGULAR tiling?
-mix of regular polygons with different numbers of sides
-all vertex types are alike (meaning all vertices have the same arrangement of shapes)
-tiling is edge-to-edge
200
Find the check digit for the airline ticket number 10540897001X
X=5
(Scheme: Check digit is the remainder of the number after division by 7)
200
Using the Caesar cipher, encode the message MIDTERM.
PLGWHUP
200
Do bit-wise addition AND find the distance between these binary strings:
1101100
0100101
Draw a figure that has rotational but no reflectional symmetry
Draw, check conditions
200
Draw a regular tiling
Check:
The only regular tilings are equilateral triangles, squares, and hexagons
300
Is 0 38000 00127 7 a valid UPC number?
Take (3*0)+(1*3)+(3*8)...+(3*7)+(1*7). If it ends in 0, it is correct.
Note that if the weighted sum of the first numbers (without check digits) does not end in 0, the check digit is the number needed to make the weighted sum end in 0.
300
Using the Vigenere Cipher using the key word GW, encode the message COLONIALS.
IKRKTEGHY
300
What is a massive denial of service (DDoS) attack and how can you avoid them?
Attackers use the command ping-t.
To avoid it, you can set up 2+ firewalls, use a honey pot/virtual honey nets, and/or set up your router to deny ping commands.
300
What is the geometric mean of 15, 22, and 59?
Cubed root of (15*22*59) = 26.9
300
Regular octagons and squares can form a semiregular tiling of the plane with
a) two octagons and one square at each vertex
b) two octagons and two squares at each vertex
c) not enough information to answer the question
A (draw it out)
400
Is 1-4292-0900-3 a legitimate ISBN?
Yes
Take (10*1)+(9*4)+...+(1*3) mod 11 = 0. If this is true, it is valid.
400
Using RSA, if you have n=85 and s=11, decode the message "49"
Decoded message = 9 (go over example, pg 552)
400
Write out the Boolean simplification for P AND NOT(Q OR R)
P AND (NOT Q) AND (NOT R)
400
A pattern that moves in exactly one direction (and its reverse) is
A strip pattern
400
True or false: a convex polygon with nine sides can tile a plane
False (Theorem pg 655: A convex polygon with seven or more sides cannot tile)
500
Is 1234 5678 2234 5678 a valid credit card number?
No (go through example)
500
Using p=7, q=17, and r = 5 in the RSA scheme, s = ?
29 (go over example)
500
Given an IP address 131.212.66.17 and subnet mask 255.255.255.0, find the network address.
131.212.66.0 (Go over example)
500
Name all the types of symmetries for a strip pattern (Hint: there are 4)
Reflection (across a line)
Rotation (around a point)
Translation (in a particular direction)
Glide reflection (across a line)
500
Draw a semi-regular tiling of the plane
Check conditions:
-regular polygons with different numbers of sides
-vertex types alike
-edge to edge