Algebra
Number Theory
Geometry
Combinatorics
Riddles/Puzzles/Fermis
100
If the 21st term of an arithmetic sequence is 43, and the 17th term is 35, what is the 1st term of this sequence?
3
100
How many positive factors does 2772 have?
36
100
Find the area of a triangle with side lengths 9, 40, 41.
180
100
How many handshakes occur among 6 people if everyone shakes hands once with each other?
15
100
There are 6 cups facing downwards, but in order to use them, Annie must turn them all facing upwards. However, she must turn over only 4 cups each time. How many turns will it take Annie to ensure all 6 cups face upwards?
3
200
Find the value of x if x^2-y^2 = 53, and both x and y are positive integers.
27
200
How many zeros are at the end of 100!?
24
200
Two circles of equal size are inscribed in a 4 by 8 rectangle such that the circles are each touching three of the rectangle’s sides. What is the area inside of the rectangle not in the circles? Answer in terms of pi
32-8pi
200
Find the number of ways Anvi can respond to messages from her 8 secret admirers if she wants to respond to Hasini and Smithi consecutively.
10080
200
A plane with 900 passengers is flying over the Atlantic Ocean. Unfortunately, the plane ran out of fuel and is crash-landing. If one passenger dies every minute, how many passengers are left in the plane after 727 minutes?
900
300
Consider the equation x^4+(x+1)^4 + (x+2)^4 = 38, find the product of its real solutions
-1
300
Let n be a positive integer, what is the sum of all possible unit digits of n!?
13
300
Right triangle DBC with a right angle at B has point A along segment BC such that the circle with diameter AB is tangent to segment CD. If AC = AB, find DB/AB.
sqrt2/2
300
Videet is hosting a party and is inviting 99 guests. Suppose that if two people are friends, then anyone friends with one of these two people will also be friends with the other. If everyone in the party are friends, what is the minimum number of friends someone in the party could have?
1
300
Five roommates have color coded outfits. During laundry day, their colors got mixed up. Each roommate ended up with a different color, which is listed below and they each claimed the following.
Roommate 1: Red - Roommate 5 stole my original color
Roommate 2: Green - Roommate 3 and I typically wear complementary colors
Roommate 3: Purple - My actual color is a combination of 2 colors here
Roommate 4: Yellow - This is my original color
Roommate 5: Blue - I usually wear a Christmas color
If it is known that there is 1 liar within the group, which roommate could NOT have been a liar? Please write the number of the roommate who could not be a liar and if there are multiple, write down the sum of the numbers.
1+3=4
400
Find the absolute difference between the minimum and maximum values of 4sinx + 3cosx.
10
400
A palindrome is a number that reads the same forward and backward, such as 43234. Compute the smallest base-10 positive integer greater than 5 that is a palindrome when written in base 2 and 4.
15
400
Suppose trapezoid ABCD has BC parallel to AD and AB = BC = CD < AD. Points E and F lie on segment AD such that <BEA = 60º and <CFD=45º and BC = DE. Find <BCA in degrees.
30
400
How many six-digit numbers that are a permutation of the digits {1, 2, 3, 4, 5, 6} are divisible by 5?
120
400
How large is the 8th fermat number (Fermat numbers are in the form of 22n+1)? Estimate! The answer you should give is the power of 10 the number is. For example, if you have 3.21 x 10^10, the answer you should give is 10.
77 (partial for 76 and 78)
500
Evaluate:
1/240
500
Given n is a two-digit positive integer and n^3 - n^2 - 100n + 100 is a multiple of 6 but not a multiple of 4 or 9. What is the maximum value of n?
95
500
Extend each of the sides of regular pentagon ABCDE so that they meet at five points, forming another larger regular pentagon. What is the ratio of the perimeter of this new pentagon to the perimeter of pentagon ABCDE? You may use cos(36º) = (1+sqrt(5))/4.
(1+sqrt(5))^2/4 or (3+sqrt(5))/2
500
Cosmo is a playing a card game where he lays out 50 cards numbered 1-50 in a row and performs the following shuffle:
Cards 1-14 each shift forward one spot and card 15 goes to card 1’s spot
Cards 16-29 each shift forward one spot and card 30 goes to card 16’s spot
Cards 31-49 each shift forward one spot and card 50 goes to card 31’s spot
How many times must Cosmo perform the shuffle to return the card layout to the original layout?
60
500
What is the ratio of the density of an average neutron star to the density of saturn? Estimate! The answer you should give is the power of 10 the number is. For example, if you have 3.21 x 10^10, the answer you should give is 10.
14 (partial for 13 and 15)