Mental Math
1 + 4 + 9 + .. 100
385
Alice has one more than 3 times as much candy as bob, and bob has 3 times as much candy as Charles. How much candy does bob have if they have 53 pieces of candy?
12
Non-overlapping regular pentagons ABCDE and ABFGH share the side AB. What is angle CBF?
144
What is the largest amount of money you can't make with an infinite amount of coins worth 3 cents and 5 cents?
7
How many ways are there to sort a line of 4 people if one of them does not want to be the last in line?
18
What is 1221 + 2112 + 1212 + 2121 + 1122 + 2211?
9999
An arithmetic and a geometric sequence each start with the terms 9 and 15. What is the difference between the 3rd terms of each sequence?
4
A triangle has side lengths 5, 5, and 6. Find the area of the triangle.
12
What is the sum of divisors of 132?
336
Bob has 6 pairs of socks in his drawer. He randomly draws 4 socks from the drawer. What is the probability that he draws 2 pairs of socks?
1/33
What is 1 + 3 + 6 + 10 + 15 + ... + 4851 + 4950?
161700
What is the sum of the roots of 2x^3 - 10x^2 + 6x + 7?
5
95
Find all the prime factors of 999999
3, 7, 11, 13, 37 (any order is acceptable)
A penguin is 5 feet away from the ocean. Every second, it has a 25% chance of moving one foot closer to the ocean. What is the expected number of seconds until the penguin reaches the ocean?
20
(41*271)*(9091*11)
1111111111
x^2 + 1/x^2 = 47
What is x^3 + 1/x^3?
322
Circle Ω1 has radius 13, and circle Ω2 has radius 15. The distance between the centers of each circle is 14. Let P and Q be the points where the circle intersects. Find PQ
24
What is the smallest number that leaves a remainder of 3 when divided by 7, 4 when divided by 9, and 5 when divided by 11?
346
Fred the frog starts at (0, 0). Every minute, he has a 50% chance of moving up and a 50% chance of moving right. What is the probability that Fred is at (3, 4) after 7 minutes?
35/128
3*5*17*257 = ?
65535
x^3 + y^3 = 90
yx^2 + xy^2 = 42
Find xy if x and y are real numbers
7
Regular Hexagon ABCDEF has a side length of 1. Let O be the center of the hexagon and let M be the center of triangle AOB. Find AM*BM*CM*DM*EM*FM
28/27
How many ordered triples of relatively prime positive integers multiply to 840?
81
How many ways are there to distribute 5 identical teddy bears and 4 identical balls among 3 different children if each child has to get at least 1 toy?
135