number theory
If n is a single digit integer and n mod 9 is congruent to 17 mod 9, then what is n?
How many ways to choose 2 items from a set of 12?
66
25
what mathematical constant is used to calculate the area of a circle?
pi (π)
what’s the only even prime number?
2
How many factors does 2025 have?
15
12
Three consecutive integers add up to 72. What is the largest of these integers?
25
Assume the circumference of the earth is 25,000 miles. Jason runs 6,250 miles north, turns 90 degrees to his right, runs 6,250 more miles, turns 90 degrees, and runs 6,250 more miles. How many miles is he from his starting point?
0
who is known as the "father of geometry"?
Euclid
A flag has 3 vertical stripes. Each stripe can be red, white, or blue, but no two adjacent stripes can be the same color. How many different flags are possible?
12
A number is increased by 20%, then decreased by 20%; what is the ratio between the value of the new and original number?
24/25 (96/100)
A regular pentagon and regular hexagon are both inscribed in the same circle. What's the maximum number of intersection points between them?
10
this Greek mathematician ran through the streets yelling “Eureka!” after discovering how to measure volume using water displacement
Archimedes
For positive integers "n" greater than or equal to 2, define g(n) to be one more than the largest proper divisor of n. For instance g(35)=8. For how many n in the range of 2 to 100, inclusive, does g(g(n))=2?
(Source: Mandelbrot)
39
The word BALLOON has 7 letters (B, A, L, L, O, O, N). How many distinct arrangements of these letters are possible if the two L’s are not next to each other?
900
If (a)+(1/a)=3, then what is (a^4)+(1/a^4)?
47
what shape is formed by slicing a cone at an angle not parallel to the base?
ellipse
who came up with the Cartesian coordinate system?
René Descartes
How many different remainders can result when the 294th power of an integer is divided by 343?(Inspired by AMC 10)
2
One ant is on each face of a cube. When a red button is pressed, the ants must move in such a way they each move to an adjacent face, and after the move, exactly one ant is on each face of the cube. In how many ways can they move when the button is pressed? Assume the ants and faces are distinguishable.
80(i think)
166^3 + 500^3 + ABC^3 = 166,500,ABC. Find ABC. (credits to Ethan Han)
333
A rhombic dodecahedron is a polyhedron with 12 congruent rhombic faces. How many vertices does a rhombic dodecahedron have? (Inspired by AMC 10)
14
what famous irrational number starts with 2.718...?
e (Euler's number)