Math Puzzle Number 1

I promise a Math Circle coffee cup to the first person who answers this question. You can post your answer on the blog.

Problem 1 for Math Teachers’ Circle:

Given that 40! = abc def 283 247 897 734 345 611 269 596 115 894 272 pqr stu vwx

Find p;q; r; s; t;u;v;w;x, i.e. the last nine digits of the number. Be sure to explain how your answer was determined without the aid of a calculator.

Extra just for fun: Find a;b;c;d;e; f , i.e. the first six digits

Preview of our Second Meeting, October 8

In order to make attendance a little easier for many of you I am hoping to start alternating the locations of our meetings. I have asked Alina if we can meet at Paisley. I will let everybody know as soon as that is confirmed.

At the October 8 meeting we will continue our investigation of Sickle Cell Anemia. Using a little bit of probability and algebra we will be able to make some predictions that fit the "real world" quite well. People who missed our experimental session on September 10 can easily participate in this part of the project. They are related but do not depend on each other.

I really enjoy this particular project because I think it is a great example of how powerful mathematics can be when we learn to apply the fundamental ideas that we teach in middle and high school.

First Meeting on September 10

Thanks to all who attended our very first meeting. Our main activity was a probability experiment that attempts to predict what percentage of the gene pool will be composed of genes for Sickle Cell Anemia. We labeled the recessive Sickle Cell gene as "a" and the dominant Normal gene as "A". We assumed that Sickle Cell Anemia is 100% lethal, we assumed that Malaria is 50% lethal for those who of type (A,A), and that people of type (A,a) have normal blood and are resistant to malaria. Using cups and beads to model genes and gene pools, and a coin flip to model the chances of surviving Malaria, we broke into groups to model several generations of a small population. Most of the groups found that the percentage of Sickle Cell genes ranged between 20 and 40 percent, although we did have one group where the Sickle Cell gene completely disappeared from the populations. The link below will take you to the instruction sheet that we used for this exercise.

Experimental Instructions

After each of our meetings I am hoping to hear comments and suggestions from all of you. This cooperation between Paisley, Parkland and WFU is just getting started, so I want to listen to your comments and then adapt until we arrive at a best possible set up. One change that we are likely to make for our next meeting is location. Perhaps we can meet at Paisley next time, and Parkland the time after that.

Problem #1