Combinatorics
Number Theory
Geometry
Algebra
100
Thomas has 4 digits: 1, 5, 6, 8. How many distinct 4-digit integers can he make?
What is 24?
100
The number of positive integers less than 1000 divisible by neither 5 nor 7 is:
What is 686?
100
Rectangle ABCD is tangent to the circle with center D at point B. If AD = 4 and CD = 3, what is the area of the shaded region? (closest integer, calculators allowed)
What is 8?
100
What is log2(64) * log4(64)?
What is 18?
200
How many unique ways are there to arrange the letters in the word CANNON?
What is 120?
200
Using the digits 1, 2, 3, 4, 5, 6, 7, and 9, form 4 two-digit prime numbers, using each digit only once. What is the sum of the 4 prime numbers?
What is 190?
200
In the regular octagon pictured below, what fraction of the figure is shaded?
What is 1/4?
200
What is the value of a for which 1/log2a + 1/log3a + 1/log4a?
What is 24?
300
Andrew and Beatrice practice their free throws in basketball. One day, they attempted a total of 105 free throws between them, with each person taking at least one free throw. If Andrew made exactly 1/3 of his free throw attempts and Beatrice made exactly 3/5 of her free throw attempts, what is the highest number of successful free throws they could have made between them?
What is 59?
300
The largest number by which the expression n3 - n is divisible for all possible integral values of n, is:
What is 6?
300
A 3x3x3 cube has three holes passing completely through it, each with 1x1 cross-section in the center of each face. What is the total surface area in square units of the resulting solid?
What is 72?
300
Determine the smallest integer value of n for which n2 + 6n + 24 is a perfect square.
What is -10?
400
Let 
What is the ratio of the sum of the odd divisors of 
to the sum of the even divisors of 
What is 1:14?
400
Given that (((3!)!)!)/3! = k * n!, where k and n are positive integers and n is as large as possible, find n + k.
What is 839?
400
Quadrilateral ABCD has two right angles at A and C. Points E and F are on diagonal AC such that BF and DE are perpendicular to AC. If AE = 3, DE = 5 and CE = 7, what is the length of BF?
What is 4.2?
400
If the cubic equation x3 − 10x2 + px − 30 = 0 has three positive integer roots, determine the value of p.
What is 31?
500
A cube has six faces. Each face has some dots on it. The numbers of dots on the six faces are 2, 3, 4, 5, 6, and 7. Harry removes one of the dots at random, with each dot equally likely to be removed. When the cube is rolled, each face is equally likely to be the top face. What is the probability that the top face has an odd number of dots on it?
What is 13/27?
500
Find the number of ordered pairs of positive integer solutions (m, n) to the equation 20m + 12n = 2012.
What is 34?
500
A tetrahedron is a 3D solid the shape of a pyramid with a triangular base. It can be constructed by drawing a triangle ABC in the plane, then placing a point D in space such that it isn't in the same plane as ABC, and connecting D to the points A, B and C.
If the corners of a tetrahedron are cut such that a triangle forms in each corner, what is the maximum number of edges in the resulting solid?
What is 18?
500
What is the value of log280/log402 - log2160/log202?
What is 2?
600
An urn contains one red ball and one blue ball. A box of extra red and blue balls lie nearby. George performs the following operation four times: he draws a ball from the urn at random and then takes a ball of the same color from the box and returns those two matching balls to the urn. After the four iterations the urn contains six balls. What is the probability that the urn contains three balls of each color?
What is 1/5?
600
If (k+2)(x^2+y^2)>=2(x+y)^2 holds for all real numbers x and y, then what is the minimum possible value of k?
What is 2?
600
An isosceles right triangle is removed from each corner of a square such that a rectangle remains. The removed triangles are shaded in the picture below. If the sum of the areas of the shaded triangles are 200 square units, what is the length of diagonal d?
What is 20?
600
Let 
What is (1+a+b+c)/c?