Arithmetic
What is \(1+3+9+27+...+3^{10}\)?
88573
If a cube has volume 16, what is the volume of a cube with twice the side length?
128
How many different cookies can be made with 7 types of dough and 3 toppings? Cookies can also be gluten free or have gluten.
42
How many factors does 144 have?
15
Compute \(\sin(60°F)\)
Illegal and immoral
What is \(\frac12\cdot\frac23\cdot\frac34\cdot\ldots\cdot\frac{2025}{2026}\)?
\[\frac1{2026}\]
What is the sum of the angles in a dodecagon (12-sided polygon)?
1800
How many ways can you list 5 cookies from favorite to least favorite?
120
What is the largest n such that \(\frac{60^n}{n!}\) is an integer?
6
\[\int \frac{d(\text{cabin})}{\text{cabin}}\]
\[\int \frac{d(\text{cabin})}{\text{cabin}} = \ln(\text{cabin}) + C = \text{Houseboat}\]
What is the sum of every odd, positive integer up to 100?
2500
A sphere has surface area 24. What is the area of a circle with the same radius?
6
Choose a random positive integer up to 1000. What is the probability that one of its digits will be 9?
0.468559
What is the sum of all x for which
\(|x(x+2)(x+4)|\) is prime? (Hint: prime numbers are multiples of only 1 and themselves).
-4
How do you trisect an angle using a compass and straightedge?
\[\tilde\infty\]
What is \(\frac15+\frac1{25}+\frac1{125}+\ldots\)?
\[\frac14\]
What is the area of a triangle with side lengths 4, 6, and 8?
\[3\sqrt{15}\]
How many ways are there to rearrange the letters in MATHLETES?
181440
What is the remainder when \(5^{2026}\) is divided by 26?
25
\[26e^{-4}-e^{-\frac\pi4}\left(\frac{\pi^2}{16}+\frac\pi2+2\right)\]
If the sum of the first n integers is 2,053,351, what is \((n+\frac12)^2\)?
4106702.25
What is the area of a regular hexagon with side length 4?
\[32\sqrt3\]
How many ways are there to choose positive integers a, b, c, and d such that \(a+b+c+d=9\)?
56
What are the last 3 digits of \(9\cdot99\cdot999\cdot9999\cdot\ldots\cdot(99\ 9's)?\)
109
Compute \(\displaystyle\sum_{n=1}^\infty\frac1{n^2}\)
\(\frac{3141²}{6}\) points