Count Like A Pro Basic

Video tutorial

Lecture Notes

In order to become a counting expert, you must:

• be able to use counting language to describe a problem
• be familiar with various well-known patterns and techniques

Let's use lawyers as an unscientific analogy. A lawyer must be able to present a case to the judge using professional language (the "legal language") and quoting relevant laws and precedents (the "well-known patterns").

As explained in the video tutorial, being able to speak the counting language is not merely to look good. Instead, it extracting the key information, which makes the following problem solving easier. This is very similar to how a seasoned lawyer can win a case in court.

Essentially, many competition problems are the same. As such, the ability to identify the essence of a given problem and ignore irrevelant noise plays a key role in becoming an expert.

The most basic and important counting languge is:

Select $k$ out of $n$ objects, order (is / is not) important.

In a more complex case, it may be neccessary to describe whether these objects are distinguishable or indistinguishable. Such situations will be discussed later, for example in the lessons Permutation and Combination Combined, Balls in Boxes and so on.

Examples

 (2521) How many triangles are there in the following diagram?