# 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:

- Describe the magic effect carefully. Pay attention to the order in what the piles are picked up.
- Given a card at position x, define a function giving the new position of x when the cards are dealt out only once.
- 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.
- What is the situation when the pile with the chosen card is picked up in first place?
- 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.

## 3 Grading

This projects counts 0.13 of your final grade.

## 4 Questions and Office Hours

I am willing to answer your questions during my office hours.