Algebra
Geo
Combinatorics
Number Theory
Random Math Trivia
100
Charles has 
quarters and Richard has q+5 quarters. The difference in their money in dimes is:
10(q-1)
100
A chord which is the perpendicular bisector of a radius of length 12 in a circle, has length
12 root 3
100
Star flips a quarter four times. Find the probability that the quarter lands heads exactly twice.
3/8
100
The number of digits in the number 
is
10
100
This special right triangle has side lengths in the ratio 1 : √3 : 2.
30-60-90 triangle
200
The sum of three numbers is 
. The ratio of the first to the second is 
, and the ratio of the second to the third is 
. The second number is:
30
200
In 
with right angle at 
, altitude 
and median 
trisect the right angle. If the area of 
is 
, then the area of is
4K
200
How many line segments have both their endpoints located at the vertices of a given cube?
28
200
How many positive integers 
satisfy the following condition:
125
200
This shape has the most sides of any regular polygon that can be constructed using only a compass and straightedge and has fewer than 20 sides.
Regular 17-gon
300
How many ordered pairs of integers 
satisfy the equation 
?
3
300
A circle of radius 
is inscribed in a right isosceles triangle, and a circle of radius 
is circumscribed about the triangle. Then 
equals
1+root2
300
Using the letters 
, 
, 
, 
, and 
, we can form five-letter "words". If these "words" are arranged in alphabetical order, then the "word" 
occupies position
115
300
In the following equation, each of the letters represents uniquely a different digit in base ten:
The sum 
equals
21
300
This probability distribution forms a symmetric “bell curve.”
Normal distribution
400
Given that 
and 
, what is the largest possible value of 
?
1/2
400
A circle with radius is tangent to sides 
and 
of rectangle 
and passes through the midpoint of diagonal 
. The area of the rectangle, in terms of , is
8r^2
400
A palindrome between 
and 
is chosen at random. What is the probability that it is divisible by 
?
1/5
400
Let be the set of the 
smallest positive multiples of 
, and let 
be the set of the smallest positive multiples of 
. How many elements are common to and ?
668
400
This 19th-century mathematician developed non-Euclidean geometry independently and was so worried about controversy that he delayed publishing his work.
Carl Friedrich Gauss
500
How many ordered triples of integers 
, with 
, 
, and 
, satisfy both 
and 
?
2
500
A piece of cheese is located at 
in a coordinate plane. A mouse is at 
and is running up the line 
. At the point 
the mouse starts getting farther from the cheese rather than closer to it. What is 
?
10
500
Let (
, 
, ... 
) be a list of the first 10 positive integers such that for each 
either 
or 
or both appear somewhere before 
in the list. How many such lists are there?
512
500
How many ordered pairs 
of positive integers, with 
, have the property that their squares differ by 
?
4
500
A standard piece of paper can only be folded seven times, but mathematically, if you could fold it n times, it would be as thick as the observable universe. What is n?
103