Combinatorics
Johnny is hosting a game show, and the contestants have to flip a coin. In order to win, the # of heads has to equal the # of tails, what is the optimal # of times the contestants should flip the coin.
2 (or 0 if you are cringe about it)
Three vertices of ABC are (-2,1), (3, -1), (5, 1). Find th equation of the median passing through A.
y = -1/6x + 4/6
If a^3+b^3 = 217, a+b = 7. Then ab = ?
6
What is (61^2 − 39^2) ÷ (51^2 − 49^2)
11
James Garfield, the 20th president of the United States, came up with his own proof of a famous theorem based on trapezoids. What was this famous theorem?
pythagorean theorem
What is the largest integer that cannot be expressed as the sum of combinations of 13 and 7? Double points for the general form for coprime numbers m,n.
71 ,mn-m-n
For what θ does the system of equations xcosθ + ysinθ = 1 and xsinθ - ycosθ = 2 have solutions
All θ
Kevin, the farmer, has three identical fields full of grass with cows on them. The grass on the fields grows at a constant rate, and the cows eat the grass at a constant rate. Field one has 10 cows, and they ate all the grass in 80 days. Field two has 20 cows, and they ate all the grass in 30 days. If field three can sustain the cows indefinitely, at most how many cows are on it?
4 cows
When 3361 and 4705 is divided by natural number n, the remainders are both 1. Find the largest possible value of n.
672
In geometry, what term describes two lines that are not parallel, yet do not intersect with each other?
Skew
Let A and B be two finite sets, with |A|=10 and |B|=10. How many distinct functions (mappings) can you define from set A to set B, f: A→B?
10000000000
What 3D geometric shape is a Pringle?
Hyperbolic Paraboloid
x(x-3) = -1, What is x^3(x^3-18)?
-1
How many zeros are at the end of 1000!
249
What is the type of number, named after an arrogant figure in Greek mythology, where the number is equal to each of its digits raised to the same degree? (153 = 1^3+5^3+3^3)
Narcissistic Number
33
What theorem states that for every positive integer n, given n measurable objects in n-dimensions, each one can be cut in half by an (n-1) dimensional hyperplane.
2^x = x^32. Find x
256
Because they are 1 less than a power of 2, the numbers 31, 8191, and 2305843009213693951 are all what specific kind of prime numbers?
Mersenne Primes
Which brilliant mathematician often claimed that the insights for his work came to him in dreams, often involving the goddess Namakkal Devi?
Srinivasa Ramanujan
There are 12 slots in a line and 5 balls, how many ways can you place the balls such that no two are adjacent.
56
Find HG/GO where O is the circumcenter, H is the orthocenter, and G is the centroid.
2
If x^2 + x + 1 = 0, Find the value of x^49 + x^50 + x^51 + x^52 + x^53
Find all integers n such that (2^n-1)(5^n-1) is a perfect square.
0, 1
This famous unproved conjecture states that repeating two siple arithmetic operations will eventually transform every positive integer into 1.
Collatz conjecture or 3x+1 conjecture