The coefficient of the x^2 y^3 term in the expansion of (x + 2y)^5
What is 80?
200
The number of degrees in one interior angle of a regular pentagon.
What is 108?
200
a^2 + b^2 - 2ab(cos(theta))
What is the law of cosines?
200
!A -> !B (not A implies not B)
What is the contrapositive of A->B?
200
An isomorphism.
What is a one-to-one mapping between groups which preserves group multiplication?
300
What is the base 3 representation of the decimal number 83?
What is 10002?
300
The name, or number of sides, of the polygon whose interior angles sum to 1800 degrees?
What is a dodecagon, 12 sided polygon.
300
1, 3, 6, 10, 15
What are the first five triangular numbers?
300
K_5 and K_3,3?
What are the 2 smallest non-planar graphs?
300
Assuming no ties, the number of possible unique rankings in a contest with 5 entrants.
What is 120 (or 5!)?
400
e^(i*pi) + 1 equals what?
What is zero?
400
A geodesic
What is the shortest path between two points in a (metric) space?
400
Any real matrix whose rows, or columns, are orthogonal unit vectors.
What is an orthogonal matrix?
400
The smallest non-abelian group.
What is S_3?
400
The number of bears on an island who's only residents are penguins and bears, if there are 13 heads and 36 feet on the island?
What is 5?
500
The first decimal place where 3555/113 differs from the actual value of pi.
What is the 6th decimal place?
500
This paradoxical theorem says that the solid ball B can be decomposed into five pieces which can be rigidly rearranged into two balls, each exactly the same size and shape as B.
What is the Banach-Tarski paradox?
500
Given as a conjecture in the 17th century, this theorem was finally proved by Andrew Wiles in 1995.
What is Fermat's Last Theorem?
500
The group of rotations and reflections of the square.
What is the D_4, or dihedral group?
500
The function e^(-x^2)
What is a function which has no closed form anti-derivative.