## Modular Arithmetic: Some Advanced Tricks in Finding the Least Positive Residue

How to evaluate the least positive residue using brute force, Fermat’s Little Theorem and Chinese Remainder Theorem.

## How to Solve a System of Linear Equations with an Additional Parameter?

How to solve a system of linear equations, when a coefficient of a variable is itself a variable.

## How to Solve the Triangle with A=30°, b=40, and a=10?

How to find the angles and the side lengths of a general triangle — using the law of sines.

## Given a series of boxes and balls, what is the chance of randomly dropping the balls to fill all the boxes?

How to calculate the probability of randomly filling N balls into k boxes, by looking at the case of 2 boxes, 3 boxes, and the general case of k boxes.

## How to Solve a Logarithmic Inequality — When a Small Base is Involved?

A review on logarithm functions with base less than 1, and some key property which can be used to solve logarithmic inequalities based on it.