Number Theory
Combinatorics
Geometry
Mental math (no paper!)
Mystery
100
At the beginning of the school year, Lisa's goal was to earn an A on at least 
of her 
quizzes for the year. She earned an A on 
of the first 
quizzes. If she is to achieve her goal, on at most how many of the remaining quizzes can she earn a grade lower than an A?
2
100
Juan rolls a fair regular octahedral die marked with the numbers 
through 
. Then Amal rolls a fair six-sided die. What is the probability that the product of the two rolls is a multiple of 3?
1/2
100
A triangle has side lengths, 4, 6, and x. What is the difference between the maximum and minimum possible integer values of x?
6
100
A recipe for applesauce calls for 6 apples to make 8 servings. How many whole servings can be made if one uses 10 apples?
13
100
If you were to guess on a 40 question true / false test, what is the probability you get exactly 20 correct?
Your response will be considered correct if it is between 1/3 times and 3 times the correct answer.
~0.125
200
The two digits in Jack's age are the same as the digits in Bill's age, but in reverse order. In five years Jack will be twice as old as Bill will be then. What is the difference in their current ages?
18
200
A fair standard six-sided dice is tossed three times. Given that the sum of the first two tosses equal the third, what is the probability that at least one "2" is tossed?
8/15
200
Regular hexagon 
has vertices 
and 
at 
and 
, respectively. What is its area?
25√(3)
200
It takes Yoki 35 minutes to complete 5/6 of her homework. Assuming she works at a constant rate, how many minutes does it take her to complete all of her homework?
42
200
An ice cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the sphere. If the ice cream melts, it will exactly fill the cone. Assume that the melted ice cream occupies 
of the volume of the frozen ice cream. What is the ratio of the cone’s height to its radius?
3:1
300
Both roots of the quadratic equation 
are prime numbers. The number of possible values of 
is
1
(it's 61*2 = 122)
300
Let 
be the set of permutations of the sequence 
for which the first term is not . A permutation is chosen randomly from . What is the probability that the second term is 
, in lowest terms?
3/16
300
A square and an equilateral triangle have the same perimeter. Let be the area of the circle circumscribed about the square and 
the area of the circle circumscribed around the triangle. Find 
.
27/32
300
A 2 × 2 × 2 cube is removed from each corner of an 8 × 8 × 8 cube. What fraction of the original cube’s volume remains?
7/8
300
How long, in seconds, would it take to rollerblade from San Francisco California to Ithaca NY?
Your response will be considered correct if it is within one Fermi number (approximately an order of magnitude) of the answer.
2 * 10^6 seconds
400
The mean, median, unique mode, and range of a collection of eight integers are all equal to 8. The largest integer that can be an element of this collection is
14
(with 6, 6, 6, 8, 8, 8, 8, 14)
400
For a particular peculiar pair of dice, the probabilities of rolling , , 
, 
, 
and 
on each die are in the ratio 
. What is the probability of rolling a total of 
on the two dice?
8/63
400
An insect lives on the surface of a regular tetrahedron with edges of length 1. It wishes to travel on the surface of the tetrahedron from the midpoint of one edge to the midpoint of the opposite edge. What is the length of the shortest such trip? (Note: Two edges of a tetrahedron are opposite if they have no common endpoint.)
1
400
What is the remainder when 123,400,000,004,321 is divided by 300?
221
400
How many years would it take working for minimum wage in NY for 8 hours a day, 5 days a week to accumulate as much wealth as Elon Musk?
Your response will be considered correct if it is within one Fermi number (approximately an order of magnitude) of the answer.
7.8 million years
500
How many distinct four-tuples 
of rational numbers are there with
?
1
(it's 2005, 0, 2005, 0)
500
Each face of a cube is painted either red or blue, each with probability 
. The color of each face is determined independently. What is the probability that the painted cube can be placed on a horizontal surface so that the four vertical faces are all the same color?
5/16
500
A point 
is selected at random from the interior of the pentagon with vertices 
, 
, 
, 
, and 
. What is the probability that 
is obtuse?
5/16
500
The members of a marching band are placed in a circle and numbered consecutively. If band member 8 is standing directly opposite band member 27, how many band members are there?
38
500
Suppose July of year 
has five Mondays. Which day must occur five times in August of year ? (Both months have 31 days.)
Thursday