computation
number theory
logic
combinatorics
misc
100
Mike cycled 15 laps in 57 minutes. Assume he cycled at a constant speed throughout. Approximately how many laps did he complete in the first 27 minutes?
7 laps
100
Each row of an amphitheater has 33 seats. Rows 12 through 22 are reserved for a youth club. How many seats are reserved for this club?
363
100
You have six coins, one of which is counterfeit (lighter), and a balance. What is the least amount weighings to determine which coin is counterfeit?
2
100
A coin is flipped 3 times. How many sequences have exactly 2 heads?
3
100
What is the difference between the sum of the first 2003 even counting numbers and the sum of the first 2003 odd counting numbers?
2003
200
What is the value of 
(answer as a simplified fraction)
109/33
200
How many two-digit positive integers have at least one 7 as a digit?
18
200
The six-digit number 20210A is prime for only one digit A. What is A?
9
200
How many 4-digit numbers can you make using digits 1, 2, 3, 4, and 5 (no repeats)?
120
200
Find the sum of all integers from 1-500.
125,250
300
Real numbers a and b satisfy the equations 3a = 81b+2 and 125b = 5a-3.
What is ab?
60
300
In the expression c * ab – d, the values of a, b, c, and d are 0, 1, 2, and 3, although not necessarily in that order. What is the maximum possible value of the result?
9
300
Three boxes of coins are labeled: GOLD, SILVER, GOLD & SILVER. Each label is wrong. You may pick one coin from one box (without looking inside) to determine the correct labels for all boxes. Which box do you pick from?
GOLD & SILVER
300
How many orderings are there for 6 people to stand in a line?
720
300
The least common multiple of a positive integer n and 18 is 180, and the greatest common divisor of n and 45 is 15. What is n?
n = 60
400
The sum of three numbers is 96. The first number is 6 times the third number, and the third number is 40 less than the second number. What is the absolute value of the difference between the first and second numbers?
5
400
How many numbers from 1 to 100 (inclusive) are divisible by 2 or 7?
57
400
A box contains 28 red balls, 20 green balls, 19 yellow balls, 13 blue balls, 11 white balls, and 9 black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 15 balls of a single color will be drawn?
76
400
Out of 12 (different) projects, you need to choose 3 of them. How many different ways are there to do this? (It does not matter what order you choose them in.)
220
400
Square ABCD has side length 1. Points P, Q, R, and S each lie on a side of ABCD such that APQCRS is an equilateral convex hexagon with side length s. What is s? (answer as simplified radical)
2 - √2
500
Two lines with slopes 1/2 and 2 intersect at (2,2). What is the area of the triangle enclosed by these two lines and the line x + y = 10?
6
500
What is the least positive integer m such that 
is a perfect square?
70
500
What is the greatest number of consecutive integers whose sum is 45?
90
500
How many ways are there to arrange the letters in BOOKKEEPER? (calculator permitted)
151,200
500
A square has sides of length 10, and a circle centered at one of its vertices has radius 10. What is the area of the union of the regions enclosed by the square and the circle? (answer in terms of π)
100 + 75π