knossos games A pathogen is spreading through a small population. The green dots are those who have been infected, while the grey dots are those not infected. Pathogen Puzzle by Tim Boester The “contact chart” shows the daily interactions among the population. This pathogen takes one day to infect all those who come into contact (adjacent dots on the contact chart) with an infected person, unless they are vaccinated against the pathogen. This example shows how the infection spreads through a population over two days. Notice that those who are vaccinated do not become infected, nor do those who are more than two “contact days” away from the initial infection. 1 0 v initial infection Here is a contact chart that shows who is and is not infected. In this outbreak, the pathogen has had 5 days to spread, and only people were vaccinated. Can you determine who brought the pathogen into the population (in other words, who was the first to be infected)? 2 1 1 0 1 2 1 0 1 after one day 2 after two days Solution for Nov/Dec Knossos Games January/February 009 1: 6A 2: 6 3: 6 1: 6A 2: 5C 3: 6 1: 6A 2: 5C 3: 3E 1: 6A 2: 7D 3: 3E 1: 6A 2: 7D 3: 1B 1: 4C 2: 7D 3: 1B 1: 4C 2: 1 3: 1B 1: 1 2: 1 3: 1B Tim Boester is an Assistant Professor in Mathematics Education at Wright State University. You can find more puzzles on his website at homepage.mac. com/boester/ imagine 4
http://homepage.mac.com/boesterhttp://homepage.mac.com/boester
Table of Contents for the Digital Edition of Imagine Magazine - Johns Hopkins - January/February 2009