Decision Support Puzzles for Applied Mathematicians
February 2010 - Planet Colonization
You can download, print, and build a model of this planet here.
Colonizing a new planet where conditions are unpredictable and harsh is never easy. The primary concern when selecting a landing site for the first colony is the proximity to natural resources. Access to these valuable resources determines whether or not a new colony thrives or dies.
Figure 1 shows the front and rear views of a newly discovered planet. The planet has been divided into 20 areas, each of which is a potential landing site to establish a new colony. Some areas contain valuable resources (represented by colored icons) that are needed in order for the new colony to survive. Food is represented by the green ear of corn, Oxygen by the red O2, water by the blue drop, and energy by the orange lightning bolt.
When choosing a landing site, it is best to minimize the distance between that site and the four needed resources. Distance is calculated by the number of units it takes to get to the resource. For example, if area 9 were selected as the landing site, the total travel distance required to reach all four resources would be 6 units (2 for Energy, 1 for Food, 1 for Water, and 2 for Oxygen).
Question: Which of the 20 areas is the best landing site to minimize the total distance you would have to travel to all four resources?
Send your answer to email@example.com by April 15th, 2010. The winner, chosen randomly from correct answers, will receive an “O.R. The Science of Better” T-shirt. Congratulations to Kelli Beckley for correctly solving October’s Connected PuzzlOR. Past questions can be found at puzzlor.com.