Big Numbers
Trigonometry
Logic
System of Equations
Polynomials
100
1 followed by 100 zeros
a googol
100
Triangles △XYZ∼△PQR
XY=8, XZ=12, PQ=4
Find PR.
6
100
If it rains, the ground gets wet.
If the ground is wet, the soccer game is canceled.
It is raining.
Can we conclude the soccer game is canceled?
Yes
100
A baseball bat costs $1 more than a baseball
The combined cost of the two is $1.10
What is the price of the baseball bat
$1.05
100
State the quadratic formula
(-b ± √b² - 4ac)/2a
200
10 to the power of a googol
a googolplex
200
sin30 = ?
1/2
200
Five friends — Anna, Ben, Carla, Dan, and Eli — are sitting in a row.
Anna is next to Ben.
Carla is immediately between Dan and Eli.
Dan is at the far left.
Who is sitting in the middle?
Eli
200
2x + y = 20
x - y = 4
x = 8
y = 4
200
x² = 100
x = ?
± 10
300
A tree in which every node is labeled with one of three possible labels, counting all distinct shapes and labelings
Tree(3)
300
sin²θ + cos²θ = ?
1
300
Three people — Alice, Bob, and Charlie — each make a statement:
Alice: “I didn’t take the cookie.”
Bob: “Charlie took the cookie.”
Charlie: “Bob is lying.”
If only one statement is true, who took the cookie?
Alice
300
A concert sells adult tickets for $15 and child tickets for $10.
They sell 50 tickets and make $650.
How many child and adult tickets were sold
30 adult
20 child
300
factor 3x² + 5x - 2
(3x-1)(x+2)
400
2↑↑↑3
2 pentation 3
400
In △ ABC, ∠A=40°, ∠B = 60° and a = 10, find side b
13.5
400
Agnes writes the following four statements on a blank piece of paper.
At least one of these statements is true.
At least two of these statements are true.
At least two of these statements are false.
At least one of these statements is false.
Each statement is either true or false. How many false statements did Agnes write on the paper?
1
400
x + 2y = 10
2x - y = 3
x = ?
16/5
400
(x+1)³ = ?
x³ + 3x² + 3x + 1
500
Huge number from a hypercube edge-coloring problem
Graham's number
500
simplify
(1 - cos²θ)/sinθ
sinθ
500
There are 4 prisoners: A, B, C, and D.
They are lined up so that each prisoner can see the hats in front of them:
D sees C, B, and
C sees B and
B sees nobody
A sees nobody
Each prisoner is wearing a hat that is either black or white. There are 2 of each color
They cannot see their own hat.
A and B are on two sides of a wall, both only see the wall
- Everyone has perfect logical reasoning
Who can deduce the color of their hat first (2 answers)
D or C
500
For which value of k does the system have no solution?
kx + y = 6, 2x + ky = 12
±√2
500
factor 2x³−3x²−8x+12=0
(x-2)(x+2)(2x-3)