f(f(x)) = x^2

Find a real function f so that f(f(x)) = x^2 for all x.

x^(x^3) = 3

Find a real solution to x^(x^3) = 3.

Parabola and Circle

A circle intersects the parabola y=x^2 at the points (1,1), (2,4), and (3,9). Find the fourth point of intersection.

Sum of k(k+1)(k+2)

Calculate 1*2*3 + 2*3*4 + 3*4*5 + ... + 998*999*1000.

Last two digits of (sqrt(2)+sqrt(3))^(10^100)

Find the last two digits of the integer closest to (sqrt(2)+sqrt(3))^(10^100).

(x+y+z)^100

How many terms does (x+y+z)^100 have when expanded? (After combining like terms.)

Winning percentage

A team won 90% of their games during a season, but lost the first game. Was there a point where their winning percentage was exactly 80%? Exactly 70%?

Product of fractions

Simplify (3/4)*(8/9)*(15/16)*(24/25)*...*(9999/10000).

Polynomial remainder

Find the remainder when x^1000 is divided by x^4 - x^2 + 1.

A Fibonacci sum

Evaluate the sum of Fib(n)/10^n where Fib(n) denotes the nth Fibonacci number.

That is, calculate 1/10 + 1/10^2 + 2/10^3 + 3/10^4 + 5/10^5 + 8/10^6 + 13/10^7 + ...

Positive integer solutions to 4x + 5y < 1001

Find the number of solutions to the inequality 4x + 5y < 1001, where x and y are positive integers.

Road Trip

Sue drives from San Francisco to New York City. At the halfway point her average speed is 40 miles per hour. How fast must she drive to average 60 miles per hour for whole trip?