Forgot password? New user? Sign up
Existing user? Log in
You're on Space Station Dodecahedron (shaped exactly like a regular dodecahedron), where each vertex is a research node, and the edges are tubes which connect the nodes.
To fix a critical failure in life support systems, you must travel by connecting tubes, visiting each node of the space station exactly once, and then return to your starting node.
Is this possible?
Hint: The vertex graph of a dodecahedron is provided below.
Are you sure you want to view the solution?
A user attempting to solve a problem has only been able to determine that the answer is a 2-digit positive integer.
If the user has 3 tries to guess the answer, what is the approximate chance of getting it correctly?
Are you sure you want to view the solution?
Laurie is standing on the edge of a cliff at a height of $h$ above Orlando. Laurie runs horizontally away from Orlando at constant speed just as he throws a ball towards her. The ball reaches a height of $2h,$ and then Laurie catches the ball as it falls.
What is the ratio of Laurie's speed to the ball's horizontal speed?
Details and Assumptions:
Are you sure you want to view the solution?
An isosceles triangle $ABC$ $($with $\angle B=\angle C)$ is cut into two smaller isosceles triangles (which don't have to be identical).
How many different possible angles $\angle A$ are there?
Are you sure you want to view the solution?
In each of the cases below, there exists only one solution whereby the sum of $n$ positive integers equals the product.
If solution(s) exist for $n=5,$ find the sum of all possible sums (or equivalently, products).
If such a solution does not exist, submit your answer as 0.
Are you sure you want to view the solution?
Problem Loading...
Note Loading...
Set Loading...