# PREDICTING BY PILING

### Deadline: February, 23rd, 2011, by 11:59:59 p.m.

A pdf version of this document can be found HERE.

## 1 Project

A few days ago a magical effect based on some mathematical idea was performed in class. The student is asked the following:

1. Describe the magic effect carefully. Pay attention to the order in what the piles are picked up.
2. Given a card at position x, define a function giving the new position of x when the cards are dealt out only once.
3. Given a card at position x, define a function giving the final position of the chosen card as performed in class. Prove by using your function that the magic effect always works.
4. What is the situation when the pile with the chosen card is picked up in first place?
5. What happens if 27 cards are considered instead of 21? Does the picking-up order matter?

## 2 Written Paper

Write a paper answering the above questions. If you do it in Spanish, please, make no spelling mistakes. The paper has to be written in correct Spanish or English; it also has to possess clarity of thought. Show me what you know; do not force to search for it through a poorly written paper.
If you copy stuff from the Internet and you do not understand it, I’ll give you zero points.