The Pigeonhole Principle states that if you have $n$ pigeons and $n-1$ pigeonholes, then at least one of those holes must contain at least $\lceil{\frac{n...

I am reading a collection of problems by the Russian mathematician Vladimir Arnol'd, titled A Mathematical Trivium. I am taking a stab at this one: C...

What's the difference between stochastic and random?

What is the next number in the sequence ? 1 1 1 2 1 1 2 1 1 1 1 1 2 2 1 3 1 2 2 1 1 1 3 1 1 2 2 1

I have to find the value of $\theta$ in this equation "$\cos2\theta \sin\theta = 1$" The problem is that I have to solve using algebra (making equations.....

Take $\binom{n}{r}$. It denotes how in how many different ways you can choose $r$ elements from a set of $k$ elements. For case $\binom{4}{3}$ which evalu...

We have $u_0 = 6$ and $u_{n+1} = \dfrac{1}{2} u_n + \dfrac{1}{u_n}$. We can use our graphing calculator to make a 'web diagram' (no idea what it...

Assume that there two people working in a call centre: PersonA and PersonB. They are both waiting for calls in separate locations. I want to calculate the...

The equation for the first line is $y = \frac{1}{2}x - 2$, and the equation for the second line is $y = 2x + 1$. They intersect at $(-2, -3)$. Someone tol...

Denote by $ \sup f $ the supremum of the set of images of a function. I proved that if the values are positive, then $$ \sup \left( f \right)\sup \left( g...