Eerily Easy Derivatives
Creepy Combinatorics
Goulish Geometry
You know it or you don't
100
The derivative
d/( d t) ( t π^ 2 + e^ 3 − (1 + sqrt(t^ 2))/( | t | + 1 ))
pi^2
100
This is the number of ways to place n rooks on an n-by-n chessboard so that no two rooks could attack one another. (I.e., no pair of rooks share a row or column of the board.)
n!
100
You are 25 feet from the base of a building, and you are looking up at a bird resting on the edge of the roof at an angle of elevation of 50 degrees. This is the height of the bird relative to the ground.
25 tan 50 degrees
100
The contrapositive of the statement:
"If Jacob watches It and eats too much candy, then he will have nightmares about Pennywise."
"If Jacob does not have nightmares about Pennywise, then he did not watch It or did not eat too much candy."
200
The derivative
d /(d x) ( root2root3root4root5 x ) ^(5 !)
1
200
A bucket of Halloween candy contains 10 Reese's cups, 5 Kit-Kat's, 7 bags of Skittles, and 8 Snickers bars. If you randomly select three pieces of candy from the bucket, this is the probability of getting at least one Kit-Kat.
1-(25 choose 3)/(30 choose 3) = 1 - 115/203 = 88/203 = 0.434
200
Given a rectangle with base of 6 and height of 8, if we take the midpoints of each side and make a new figure from those points, this is the area of the new figure.
24
200
The value of
e^(ipi)
-1
300
The derivative
f^((423))(sinx)
-cosx
300
A certain Congressional committee consists of 10 members, of whom 6 are Democrats and 4 are Republicans. This is the number of ways a 6-person subcommittee consisting of exactly 3 Democrats and 3 Republicans can be chosen.
(6 choose 3) * (4 choose 3) = 80
300
If the regular hexagon below is rotated counterclockwise by 780º, this is the new position of the vertex marked E.
D
300
What is the Euler number of the following planar graph?
The Euler number of every planar graph is 2.
400
The derivative
∂^ 3/( ∂ x ∂ y ∂ z) ( x^ 3 y^ 2 + z e^ sin ( x ) + π z^ π y^ e )
0
400
Suppose that license plates in a certain state must follow be given by three letters, followed by a dash, followed by four digits. This is the total number of possible license plates.
26^3*10^4 = 175760000
400
Given a cube with a volume of 216, this is the volume of the largest possible sphere contained inside of the cube.
36pi
400
What number is equal to the following expression?
1+1/(1 + 1/(1 + 1/(1 + \ddots)))
(Hint: Call this quantity 'x' and get a quadratic equation that x must satisfy.)
The golden ration,
varphi = (1 + sqrt(5))/2
500
The derivative
d /(d x) ( e^2 )^ ln ( x/ sqrt 2 )
x
500
Suppose P1, P2, …, P8 are eight distinct points in the plane, and exactly three of these points are collinear. This is the number of (non-degenerate) triangles that can be formed using three of these points as vertices.
(8 choose 3) - 1 = 55
500
Suppose ABCD is parallelogram of area 34 with bases AB and CD having a length of 4. If AB lines on a line L1 and CD lies on a line L2, and if we shift CD five units along L2, this is the area of the resulting parallelogram.
34
500
The name of a polygon with eleven sides.
A hendecagon