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## Sunday, March 29, 2009

### The euphoria of solving a mathematics exercise.

The first part of exercise 1.10 in 'A Course in Enumeration' by Martin Aigner asks to evaluate the sum below by counting configurations of dots.
Although the answer can be simply taken from Pascal's Triangle as
C(n+1,2)+2C(n+1,3)
the challenge of the exercise was to deduce the same answer by setting up a particular configuration of dots.

To make a long story short... that's how I spent my entire free Saturday. By not finding the answer that is. I did this ( Sunday ) morning though with great relief. I was close right away but I -sort of- forgot to finish it correctly, instead I kept searching for other, better dot configurations. In the rush of having solved another 'difficult' exercise I remembered an article with the title 'Addicted To Knowledge' which explains the feeling I had.

Aigner says in the preface: 'It is commonplace to stress the importance of exercises. To learn enumerative combinatorics one simply must do as many exercises as possible.' An exercise is only an exercise if it was a challenging exercise, I would like to add. And harder means deeper in the context of exercises.

Hint to the answer: find a dot-configuration for the sum of 1,2,3,...,n first.

#### 1 comment:

1. Was the idea to stack the dots in 3 dimensions as a pyramid?

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)