Algebra
Geo
Combinatorics
Number Theory
Random Math Trivia
100
How many pairs of non-zero real numbers (a, b) exist such that the sum a + b, the product ab, and the quotient a/b are all equal?
1
100
Suppose you are given a square with side length a and an equilateral triangle with side length b such that both figures have the same area. What is the ratio of a to b?
(fourth root of 3)/2
100
Aaliyah rolls two standard 6-sided dice. She notices that the product of the two numbers rolled is a multiple of 
. Which of the following integers cannot be the sum of the two numbers?
6
100
What is the last digit of 2019^2019 ?
9
100
What is a number that has the same meaning as the number of letters it has?
Four
200
Andy rides his bike from his house to the store at 6 miles per hour. Upon arriving at the store, he realizes it’s closed and immediately heads back, riding his bike back home at a speed of 2 miles per hour. What is Andy’s average speed in miles per hour
3
200
Four circles of radius one are centered at the points (1, 1),(1, −1),(−1, −1), and (1, −1). A fifth circle is drawn centered at the origin such that it is tangent to the other four circles. What is the radius of the fifth circle?
1 + root2
200
Mr. and Ms. Zeta want to name their baby (with last name Zeta) so that its monogram (first, middle, and last initials) will be in alphabetical order with no letters repeated. How many such monograms are possible?
300
200
How many zeroes in a row occur at the end of the number 100!.
24
200
Who is considered the father of Geometry?
Euclid
300
How many ordered pairs of integers 
satisfy the equation 
?
3
300
Line segment 
is a diameter of a circle with 
. Point 
, not equal to 
or 
, lies on the circle. As point moves around the circle, the centroid (center of mass) of 
traces out a closed curve missing two points. To the nearest positive integer, what is the area of the region bounded by this curve?
50
300
How many triangles with positive area have all their vertices at points 
in the coordinate plane, where 
and 
are integers between 
and 
, inclusive?
2148
300
I have 2 numbers a and b such that a + b = c. The sum of the digits of a is 27 and the sum of the digits of b is 32. When I added a and b by hand, I had to carry 3 times. What is the sum of the digits of c?
32
300
This famous English mathematician is often credited as the inventor of calculus also had a deep interest in alchemy, spending many years of his life conducting secret experiments in the hope of discovering the fabled Philosopher’s Stone.
Sir Isaac Newton
400
A classroom has a row of 35 coat hooks. Paulina likes coats to be equally spaced, so that there is the same number of empty hooks before the first coat, after the last coat, and between every coat and the next one. Suppose there is at least 1 coat and at least 1 empty hook. How many different numbers of coats can satisfy Paulina's pattern?
7
400
Circles with centers 
and 
, having radii 
and 
, respectively, lie on the same side of line 
and are tangent to at 
and 
, respectively, with 
between 
and . The circle with center 
is externally tangent to each of the other two circles. What is the area of triangle 
?
root 6 - root 2
400
A solitaire game is played as follows. Six distinct pairs of matched tiles are placed in a bag. The player randomly draws tiles one at a time from the bag and retains them, except that matching tiles are put aside as soon as they appear in the player's hand. The game ends if the player ever holds three tiles, no two of which match; otherwise the drawing continues until the bag is empty. The probability that the bag will be emptied is 
where 
and 
are relatively prime positive integers. Find 
394
400
How many trailing zeros does the value
300 · 305 · 310 · · · 1090 · 1095 · 1100
end with?
161
400
This famous mathematician and philosopher developed the Cartesian coordinate system in the 17th-century.
René Descartes
500
Let 
be a sequence of integers such that 
and 
for all positive integers 
and 
Then 
is..
78
500
Two circles, ω1 and ω2, are internally tangent at A. Let B be the point on ω2 opposite of A. The radius of ω1 is 4 times the radius of ω2. Point P is chosen on the circumference of ω1 such that the ratio
AP/BP = 2 √3 /√ 7 . Let O denote the center of ω2. Determine the ratio OP / AO.
root 37
500
A set of 
people participate in an online video basketball tournament. Each person may be a member of any number of -player teams, but no two teams may have exactly the same members. The site statistics show a curious fact: The average, over all subsets of size 
of the set of participants, of the number of complete teams whose members are among those people is equal to the reciprocal of the average, over all subsets of size 
of the set of participants, of the number of complete teams whose members are among those people. How many values , 
, can be the number of participants?
557
500
We say that an integer x ∈ {1, · · · , 102} is square-ish if there exists some integer n such that
x ≡ n^2 + n (mod 103). Compute the product of all square-ish integers modulo 103.
52
500
Closely resembling a soccer ball, this geometric structure is comprised of interlocking hexagons and pentagons.
Buckyball