Counting
Geometry
Probability
Number Theory
Algebra
100
Leo has one book each for algebra, geometry, history, psychology, Spanish, English, and physics in his locker. If he chooses three books from his locker, how many different sets of three books could he choose?
35
100
How many equilateral triangles with side length 3 can fit into a regular hexagon with side length 9?
54
100
On a checkerboard composed of 64 unit squares, what is the probability that a randomly chosen unit square does not touch the outer edge of the board?
9/16
100
Convert 625 to base 7
1552
100
What is the value of x?
(Pictured equation: 2025^x = 3sqrt5)
1/4
200
How many arrangements of the word TRALALERO are there?
45360
200
Right triangle ABC has an area of 70 square inches, with angle at B measuring 90 °. The altitude from B to AC is 5 inches long. What is the hypotenuse of the triangle?
28 inches
200
A bag with 12 marbles contains some number of red marbles. If two marbles are drawn, there is a 6 in 11 chance that no red marbles are drawn. How many red marbles are there?
3 red marbles
200
Evaluate A211 + CB713 in base 10.
2290
200
The expression 2025/10! can be written as 2^n. What is n, rounded to the nearest integer?
-11
300
Justin's soccer team has 8 players. He has to choose a starting lineup of a goalie and 5 regular players (anyone can play goalie or be a regular player). How many different starting lineups can Justin choose?
168
300
Isosceles right triangle A has hypotenuse with side length 2√2. Right triangle B is similar to right triangle A. Triangle B's perimeter is three times triangle A's perimeter. What is triangle B's area?
18
300
What is the probability that a six sided die and a twelve sided die will roll the same number?
1/12
300
Evaluate 426 * 5316 in base 6.
355426
300
After a game went on sale for X% off, their profit increased by 100% and the total copies sold increased by 150%. What is the value of X?
20
400
How many three digit numbers can be rearranged to be divisible by 10 (or are already divisible by 10)?
171
400
What is the axis of symmetry of the function f(x) = 2^(x-3) + 2^(-x) ?
x = 1.5
400
Peter rolls three six sided dice, labeled A, B, and C. In simplest form, what is the probability that A + B = C?
5/72
400
Find the positive base a in which the equation 4a*12a = 103a is valid.
5
400
A class averages 85% on a test with 30 questions. The teacher later finds out that one question was graded incorrectly, and that X% of students were wrongly marked incorrect. After regrading the test, the class average was 86%. What is the value of X?
30
500
I have tiled my square bathroom wall with congruent square tiles. All the tiles are red, except those along the two diagonals, which are all blue (i.e. the corners are blue and all the tiles along the diagonals between each pair of opposite corners are blue). If I used 121 blue tiles, how many red ones did I use?
3600
500
Colin runs a snow cone stand. His ice machine can produce 6000 cm^3 of ice every 30 minutes. A complete snow cone consists of ice filling a conical paper cup with a hemisphere of ice on top. His snow cone cups are 15 centimeters deep and have a circular top with a diameter of 6 centimeters. How many complete snow cones can he make in an hour? (Approximate pi as 3.14)
60
500
Blake tosses one penny and Colin tosses two pennies. What is the probability that Colin gets the same number of heads that Blake gets?
3/8
500
Hexadecimal (base-16) numbers are written using numeric digits 0 through 9 as well as the letters A through F to represent 10 through 15. Among the first 1000 base 10 positive integers, how many have hexadecimal representations that only contain numeric digits? (e.g. no letters)
399
500
Three generous friends, each with some money, redistribute the money as followed: Karl gives enough money to Sam and Dao to double each of their amounts. Jan then gives enough to Karl and Dao to double their amounts. Finally, Dao gives enough to Karl and Sam to double their amounts. If Dao had 36 dollars at the beginning and 36 dollars at the end, what is the total amount that all three friends have?
252