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)
a+b+c = 19
a^2 + b^2 + c^2 = 2019
Find ab + bc + ca
-829
When 3361 and 4705 is divided by natural number n, the remainders are both 1. Find the largest possible value of n.
672
This famous Greek mathematician and author of The Elements is known as the “Father of Geometry.”
Euclid
Here's a hypothetical game: There's a pot that starts at $1. You flip a coin. Heads, you get the pot, and the game ends. Tails, you double the pot and flip again. How much money would you pay to play the game?
Mathematically, infinite
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
N is a positive integer such that n/2019 rounds to 6. Find the number of possible values of n.
2019
69421
As you might know, there is no Nobel Prize for Mathematics, instead there are many other awards. This award/medal named after a Canadian mathematician, has been described as the Nobel Prize of Mathematics and regarded as the top award in the field of mathematics worldwide.
Fields Medal
Peter Cheng, Bryan Tom, Daniel Gusak, and James Gikas are watching a movie on Valentine's Day. Peter and Bryan Tom have to sit together, and Daniel and Peter can't sit together. How many ways can they sit together?
8, Peter gave this answer so if it is wrong blame him I'm too lazy to check
tanx - 2 cotx = 1. Find the possible values of sinx
2sqrt5/5
sqrt2/2
-2sqrt5/5
-sqrt2/2
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 20 cows and they ate all the grass in 30 days. Field two has 30 cows and they ate all the grass in 15 days. If field three can sustain the cows indefinitely, how many cows are on it?
10 cows
Find the remainder when 7^2019 * 9^2020 is divided by 31
9
Each of Aiden, Bella and Chris prepared a box for Dyland. Dylan's birthday present is in one of the boxes. The teacher in advance told Dyland how many of them lied.
Aiden, "The present is in my box"
Bella, "The present is in Chris's box"
Chris, "The present is not in Aiden's box"
Dylan, under teacher's clue successfully deduced which box contains the present. Whose box is the present in?
Chris
There are 8 balls in a line. Charles needs to paint them green or yellow. Each ball must have a neighbor that is painted green; how many ways are there to paint the 8 balls?
16
This famous mathematician and philosopher developed the Cartesian coordinate system in the 17th-century
René Descartes
2^x = x^32. Find x
256
The integer n is the smallest positive multiple of 15 such that every digit of n is either 8 or 0. Find n.
88800
How many colors are needed on a map to ensure that no 2 colors share the same border
4
Professor Gable buys a lottery ticket, which requires that he pick six different integers from 1 through 46, inclusive. He chooses his numbers so that the sum of the base-ten logarithms of his six numbers is an integer. It so happens that the integers on the winning ticket have the same property. What is the probability that Gable holds the winning ticket? AMC 12 2000 Problem 23
1/5, 1/4, 1/3, 1/2, 1
1/4
Triangle ABC has right angle at B, and contains a point P for which PA = 10, PB = 6 and angle APB = BPC = CPA. Find PC.
If x^2 + x + 1 = 0, Find the value of x^49 + x^50 + x^51 + x^52 + x^53
What is the remainder upon dividing 6^83 + 8^83 by 49?
What is definitively the worst topic in competition math?
Geometry