Not Too Bad
Long Words
Getting Harder
Basically Algebra
...Huh?
100
A fair coin is tossed 3 times. What is the probability of at least two consecutive heads?
What is 3/8?
100
Andy thinks of four numbers 27, 81, 36, and 41 and whispers the numbers to his classmate Cynthia. For each number she hears, Cynthia writes down every factor of that number on the whiteboard. What is the sum of all the different numbers that are on the whiteboard? (Don’t include the same number in your sum more than once)
What is 240?
100
Ivan, Stefan, and Katia divided 150 pieces of candy among themselves so that Stefan and Katia each got twice as many pieces as Ivan received. Find the number of pieces of candy Ivan received.
What is 30?
100
The number 45,231 is a five-digit positive integer that uses five consecutive digits(excluding 0), although not necessarily in order. How many such five-digit numbers are there?
What is 600?
100
Find the sum of all integers n such that 
is also an integer.
What is 0?
200
If 
, 
, and 
, what is the product of p, r and s?
What is 40?
200
A palindrome is any number that reads the same forward and backward (for example, 99 and 50505 are palindromes but 2020 is not). Find the sum of all three-digit palindromes whose tens digit is 5.
What is 4995?
200
Find the greatest odd divisor of 1603.
What is 125?
200
A bag contains 10 blue, 4 green, and 8 red marbles. How many green marbles must be added to the bag so that 75 percent of the marbles are green?
What is 50?
200
The sides of a triangle have lengths of 15, 20 and 25. Find the length of the shortest altitude.
What is 12?
300
At a gathering of 30 people, there are 20 people who all know each other and 10 people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur within the group?
What is 245?
300
Neethine the Kiwi says that she is the eye of the tiger, a fighter, and that everyone is gonna hear her roar. She is standing at point (3, 3). Neeton the Cat is standing at (11,18), the farthest he can stand from Neethine such that he can still hear her roar. However, both of them don't know Neethine can still make sounds even farther away. At two points at the edge of her roaring range such that they form a 120-degree angle with Neethine, she can make sounds for an additional 5 miles beyond her roaring range. What is the total region that Neethine can make sounds?
What is 354 pi?
300
Gwendoline rolls a pair of six-sided dice and records the product of the two values rolled. Gwendoline repeatedly rolls the two dice and records the product of the two values until one of the values she records appears for a third time. What is the maximum number of times Gwendoline will need to roll the two dice?
What is 37?
300
The perimeter of a rectangle is 40 inches and each diagonal of the rectangle is 18 inches long. What is the area of this rectangle?
What is 38?
300
How many ways are there to answer a 10-question true/false test, where at least 3 of the questions have been answered with a false?
What is 968?
400
An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is 4, what is the area of the hexagon?
What is 6?
400
In the quarterfinals of a single elimination countdown competition, the 8 competitors are all of equal skill. When any 2 of them compete, there is exactly a 50% chance of either one winning. If the initial bracket is randomized, what is the probability that two of the competitors, Daniel and Anish?
What is 1/4?
400
Find the number of positive integers less than or equal to 2019 that are no more than 10 away from a perfect square.
What is 829?
400
For a particular sequence, the first term, an, is 1, and for every term thereafter, the value of the nth term is given by an = an-1 + 2n. What is the value of a100
What is 10099?
400
Find all real numbers x such that 8x3-108x2+486x-729=25+2(5)(3)+9. Express your answer as a decimal
What is 6.5?
500
How many perfect cubes lie between 28+1 and 218+1, inclusive?
What is 58?
500
Find the smallest positive integer that leaves a remainder of 2 when divided by 5, a remainder of 3 when divided by 6, a remainder of 4 when divided by 7, and a remainder of 5 when divided by 8.
What is 837?
500
Find the greatest integer n such that 5n divides 2019! − 2018! + 2017!.
What is 504?
500
What is the value of sqrt(11,111,111× 100,000,011 + 4)?
Reminder: *no calculators*!
What is 33333335?
500
The real root of the equation 
can be written in the form 
, where a,b,c are positive integers. Find 
.
What is 98?