CEMC Beaver Computing Challenge (BCC)
In a stack of books, you can only add a book to the top or remove a book from the top. What standard computer science data structure operates on this exact Last-In, First-Out (LIFO) principle?
Stack.
A line passes through the origin (0,0) and the point (6, 12). What is the slope of this line?
2
What is the remainder when 2^100 is divided by 7?
2
Why was the math textbook always sad?
Because it had too many problems.
In the popular mobile game 2048, what mathematical property do all starting and merged tile numbers share?
They are all powers of 2
A beaver wants to move through a network of pipes. The maximum water flow from the source to the sink is constrained by the narrowest pipe in any given path. What classical graph theory problem does this scenario represent?
Max-Flow Problem (or Bottleneck Shortest Path).
What is the positive integer value of x that satisfies the equation x2 + 5x - 36 = 0?
x = 4
The sum of an infinite geometric series is 16, and its first term is 12. What is the common ratio r?
r = 1/4
Parallel lines have so much in common, but why is it so tragic?
Because they will never meet.
If you are playing the game Monopoly and roll two standard six-sided dice, what is the single most probable total sum you will roll?
7
A robot follows instructions: MOVE_FORWARD, ROTATE_RIGHT 90°, MOVE_FORWARD. If the robot executes this entire sequence 4 times starting facing North, what is its final facing direction?
North
In a right-angled triangle △ABC with ∠B = 90°, side AB = 9 and hypotenuse AC = 15. What is the area of △ABC?
54
If log_2(x) + log_4(x) = 6, what is the exact value of x?
x = 16
What did i say to pi, and what did pi reply back?
i said "Get real!", and pi said "Be rational!"
n the classic 3x3 Rubik's Cube, what is the term for the maximum number of moves required to solve any random position, which was proven in 2010 to be exactly 20?
God's Number
A beaver uses parity bits to check for transmission errors. A row of 7 binary digits 1 0 1 1 0 1 0 gets an 8th parity bit added at the end so that the total number of 1s is even. What is the value of the 8th bit?
0
A list of five positive integers has a mean of 12, a median of 10, and a unique mode of 8. What is the maximum possible value of the largest integer in the list?
25
Two fair 6-sided dice are rolled. What is the probability that the sum of the two numbers shown is a prime number?
15/36 or 5/12
What is the term for a 3D shape formed by taking a 2D circle and revolving it around an axis in 3D space that does not intersect it — essentially a mathematical doughnut?
Torus.
Which famous mathematical constant appears hidden in the background of multiple episodes of The Simpsons, whose writers famously hold advanced degrees in math and computer science?
Euler's identity or pi
Beaver Deana enters a tree-like maze to collect dolls. To explore every possible branching path systematically by visiting deep paths first before backtracking, which depth-first search (DFS) traversal order visits the left subtree, the root, and then the right subtree?
In-order traversal.
How many ordered pairs of positive integers (a, b) satisfy the equation 1/a + 1/b = 1/6?
9
In triangle ABC, the side lengths are a = 5, b = 6, and c = 7. What is the exact value of cos(A)?
5/7