Algebra
11j + 2 = 57, j = ?
5
The definition of the orthocenter of a triangle
where all the altitudes intersect
What are the odds of flipping a coin four times and getting 4 heads?
1/16
Given 4 numbers: 6, 3, 12, 12, make the number 24 using only addition, subtraction, multiplication and division.
(12-6) * (12/3)
This holiday is celebrated on March 14th
Pi day
log2.5 in terms of a and b, if a = log5 and b = log2
b-a
The sum of the interior angles in a hexagon
270dg
Six friends meet up at a movie theater. If everyone shakes hands with each other exactly once, how many handshakes occur?
15
There are two doors before you. One leads to freedom, and one leads to a trap. A sign above the two doors says: “Only one of these statements is true. (1) The left door leads to freedom. (2) Both doors lead to freedom.” Which door should you go through?
You are the owner of a hotel that has recently just been renovated to have infinite rooms. Who was the mathematician that helped make this possible?
David Hilbert
A newly discovered bacteria triples in size every 4 hours. If a scientist has a culture with initially 50 bacteria, after 12 hours, how many bacteria will the scientist have?
1350
A cube with volume 64 cm^3 is cut into 8 equal pieces. What is the surface area of one of the smaller cubes?
24 cm^2
What is the remainder when 2^10 is divided by 7?
2
You have two ropes. Each burns completely in exactly one hour. However, they are different lengths and thus burn at different rates. Also, along each rope the width & material changes, so they burn at different rates at different places. The only thing you know is that they each burn completely in one hour exactly. You have a lighter. How do you measure exactly 45 minutes?
Light both ends of rope 1 and one end of rope 2
Once rope 1 burns completely (meaning 30 min has passed), light the other end of rope 2
Newton had beef with this person (include the why)
Hooke (for gravity) or Leibniz (for calculus)
The product of all solutions of p, if |2p - 5| = 9
-14
The number of edges a mysterious convex 3D shape with 12 faces and 20 vertices has
30
You have a spinner labeled 1-10, and you spin it at most two times. If you get an odd number the first time, you win $2 and stop. If you get an even number, you spin again. If that second number is odd, you win $4. What is the expected monetary value of playing this game?
$2
You have 9 coins that look identical, but you know one is counterfeit and weighs slightly more than the others. What is the minimum number of weighings to figure out which coin is fake? You only have a balance scale.
2
This person was the first to calculate Earth’s circumference
Eratosthenes
What x equals to, if x^x^x^x… = 2
sqrt2
An equilateral triangle is inscribed in a circle with radius 2. What is the area inside the circle but outside of the triangle?
4pi - 3sqrt3
The town of Littlepopulation has 5 houses, all of which are interconnected by roads. How many distinct roads can you take to visit all 5 houses exactly once, given you always start and stop at the same houses (i.e. House A and House E)?
6
Three ants are placed on the vertices of an equilateral triangle. At the same time, they all pick a random direction and start walking along an edge. What is the probability no ant collides with each other?
1/4
Established in the year 2000, this set of seven unsolved problems each carries a $1 million reward for each solution. Only one has been solved so far.
Millennium Prize Problems