Boring with writing
Boring with pictures
Extremely Boring
Slightly Interesting
Fun
101
For real numbers 
and 
, define 
. What is 
?
-72
101
The two legs of a right triangle, which are altitudes, have lengths 
and 6. How long is the third altitude of the triangle?
3
101
How many positive cubes divide 3!⋅5!⋅7!?
6
101
The least common multiple of a positive integer n and 18 is 180, and the greatest common divisor of n and 45 is 15. What is the sum of the digits of n?
6
101
Of A and B this is the lore:
When added they make 24.
If A over 3,
is A over B,
What's A + 2B plus 2 more?
How many solutions, you implore?
1 or 2, I forgor...
29 or 50
201
Let 
and 
denote the solutions of 
. What is the value of 
?
0
201
Consider the rectangle ABFE as shown in the figure below. ABCD is a square. If CG = 1 and GD = 2, then what is the perimeter of the rectangle ABFE?
15
201
Coin A is flipped three times and coin B is flipped four times. What is the probability that the number of heads obtained from flipping the two fair coins is the same?
35/128
201
For how many (not necessarily positive) integer values of 
is the value of 
an integer?
9
201
In this magic square, there is exactly one way to fill the empty squares so that every row, every column, and both main diagonals add up to the same value. What is that value?
21/2
301
Draw the circle x2 + y2 = 1, then draw the line through the "North Pole" (0,1) meeting the x-axis at (2,0). What is the x coordinate of the other point where the line meets the circle?
4/5
301
The centers of the faces of a right rectangular prism (dimensions 3x4x5) are joined to create an octahedron. What is the volume of this octahedron?
10
301
A player pays $5 to play a game. A die is rolled. If the number on the die is odd, the game is lost. If the number on the die is even, the die is rolled again. In this case the player wins if the second number matches the first and loses otherwise. How much should the player win if the game is fair? (In a fair game the probability of winning times the amount won is what the player should pay.)
$60
301
Claudia has 12 coins, each of which is a 5-cent coin or a 10-cent coin. There are exactly 17 different values that can be obtained as combinations of one or more of her coins. How many 10-cent coins does Claudia have?
5
301
FREE POINTS!!!
FREE POINTS!!!
401
What is the length of the shortest path that starts at (2, 1), touches the x-axis, then returns to some point on the line y = 1/2 x?
sqrt(80)/5
or
4sqrt(5)/5
401
A wire is cut into two pieces, one of length "a" and the other of length "b". The piece of length "a" is bent to form an equilateral triangle, and the piece of length "b" is bent to form a regular hexagon. The triangle and the hexagon have equal area. What is a/b?
sqrt(6)/2
401
When 7 fair standard 6-sided dice are thrown, the probability that the sum of the numbers on the top faces is 10 can be written as 
where n is a positive integer. What is n?
84
401
Define a sequence recursively by 
and 
the remainder when 
is divided by 
for all 
Thus the sequence starts 
What is 
9
401
Mr. League hosts a banquet for Walton STEM staff. The table is a square that can seat 2 people on each side, and each seat is numbered from 1 to 8. A red tablecloth is put on one half, and a blue tablecloth is put on the other half. 4 staff and 4 spouses arrive. Staff must sit on the red side, and the spouses must sit on the blue side. If staff are not allowed to sit next to their spouses, how many unique seating arrangements are possible?
336 (might be wrong)
501
Suppose that 
is an arithmetic sequence with
What is the value of 
0.01
501
Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of △ABC?
1/5
501
Three distinct vertices of a cube are chosen at random. What is the probability that the plane determined by these three vertices contains points inside the cube?
4/7
501
Elmo makes N sandwiches for a fundraiser. For each sandwich he uses B globs of peanut butter at 4 cents per glob and J blobs of jam at 5 cent per blob. The cost of the peanut butter and jam to make all the sandwiches is $2.53. Assume that B, J, and N are positive integers with N>1. What is the cost of the jam Elmo uses to make the sandwiches?
$1.65
501
Let ∆ represent the difference between the largest possible sum and the smallest possible sum of all visible faces on a dice configuration. Imagine a construction like the one below but where the number of ’holes’ is not 5 but some larger number g. If ∆ = 492 for that construction, what is the number of holes (g)?
47 holes