Thinking Analytically

The 2012 analytics treasure hunt

Five analytics puzzles, one coordinate, one $100 cash prize.
Brought to you by www.puzzlor.com

By John Toczek

If you’re a fan of the “Thinking Analytically” column or just puzzles in general, a challenging new contest will put your analytics skills to the ultimate test.

Below are a series of five puzzles that focus on common problems encountered in the mathematics, statistics and operations research fields. Each puzzle requires a specific solution methodology that you have likely acquired during your education and career.

Once you have solved each of the puzzles, place the answers into the corresponding latitude and longitude as indicated:

Input solution here:

Latitude _ _. _ _ _ _ _,
A B . C D E F G
Longitude -_ _. _ _ _ _ _
H I . J K L M N

A $100 cash prize is hidden at these coordinates. There is no entry fee and anyone can participate. Additional information can be found in the “Instructions, rules and notes” section at the end of this article and at www.puzzlor.com.

Puzzle #1 - SurvivOR

Table 1: Necessities for survival in the wilderness.

Getting lost while hiking in the wilderness is a dangerous situation. And making your way back to civilization is a difficult task that uses up resources quickly. What you decide to take with you while making the journey back to civilization can determine life or death.

Table 1 shows all of the items that are available to you that will aid you in your hike out of the wilderness. Containers of Food and Water will give you energy, Shelter will protect you from the elements, and Defense will protect you from wild animals. Each item has a weight indicated by the red number and each item has survival points indicated by the green number. You must take exactly one item from each of the four categories (Food, Water, Shelter, Defense). Unfortunately, the backpack you have has a maximum capacity of 25 kg. Your chance for survival is calculated by adding all of the survival points together from the items you choose to take with you.

Question: What is the maximum number of survival points you can achieve?

Answer No. 1: _ _ points
H A

Puzzle #2 - Choose Your Crew

Table 1: Can you pick the right crew for the voyage?

Successfully navigating the waters during sea voyages is a challenging task. A captain’s most important decision is selecting the right crew for the voyage. A mix of different skill sets is required to sail the ship efficiently, navigate to the destination and fish for food along the way.

Table 1 shows a list of crew members who are available for you to hire for the voyage. Each crew member demands a salary for the voyage and has different skill levels of Fishing, Sailing and Navigation.

In order for your journey to be successful, you must have a cumulative skill of 15 or more in each of the three skill categories from all of your chosen crew members. You may choose as many crew members as you like.

Question: What is the minimum achievable cost for the voyage?

Answer No. 2: _ , _ _ _
I J B C

Puzzle #3 - Traveling Spaceman Problem

Table 1: So many galaxies to visit, so little time.

Table 1 shows a list of galaxies that you, as the traveling spaceman, wish to visit. The table shows the coordinates in three-dimensional space where each galaxy exists in the universe.

Question: In what order should you visit each galaxy to minimize the traveled distance? You must visit each galaxy and you cannot visit any galaxy more than once.

Answer No. 3 : _ -> _ -> _ -> _ ->
                         K     E              L
                         _ -> Z8 -> L3
                         D

Puzzle #4 - Connected and Infected

Figure 1: How long until half the world is infected?

Disease can spread quickly in a globalized world where increased travel raises the opportunity for transmission. Figure 1 shows a modified map of the world divided into five areas. The arrows show the potential path for the spread of disease. For example, the Blue area can transmit infections directly to the Red and Violet areas but not to the Yellow or Green areas. Each area can also transmit disease to its own population, indicated by the arrows that circle back onto themselves.

The populations for each area are as follows: Blue has 0.5 billion people, Red has 0.5 billion people, Violet has 4.0 billion people, Yellow has 1.0 billion people and Green has 0.5 billion people. Initially everyone is healthy except for 10,000 people in the Blue area who are infected with a virus.

Each month, 6.1 percent of the infected people transmit the virus to healthy people along each transmission route. For example, at the end of month 1, the Red and Violet areas will each have 610 infected people (10,000 infected people from the Blue area x 6.1 percent) and the Blue area will have 10,610 infected people (10,000 who were originally infected plus 10,000 x 6.1 percent from infecting its own population). Infected people stay infected and no deaths occur in this scenario.

Question: After how many months is at least half of the world’s population infected?

Answer No. 4: _ _ Months
F M

Puzzle #5 - Relief Mission

Figure 1: Which two drop locations are optimal?

Coordinating relief efforts after catastrophes such as civil unrest and natural disasters can be a logistically complex challenge. Delivering relief to people in need is the immediate focus of any disaster management plan.

The map in Figure 1 shows the locations of 20 villagers, each represented by a “hut” icon. The villagers are in need of relief supplies contained in the crates attached to parachutes. There are two identical relief packages available. The only delivery option is by air drop. Each package can be dropped on any cell.

After the crates are dropped, each villager will walk to the nearest drop location to pick up relief supplies. Use a direct line between cells to calculate travel distance. For example, the distance between a1 and a2 is 1km and the distance between A1 to B2 is 1.41 km. Assume that each crate contains an unlimited amount of relief supplies.

Question: Which two drop locations will minimize the total distance that all villagers must travel?

Answer No. 5: _ _ , h _
G N

Instructions, rules and notes

Instructions
Solve the five puzzles in this document and place their answers in the latitude and longitude spaces indicated. When the puzzles are correctly completed, and the answers are placed in the corresponding latitude and longitude slots provided at the beginning of this article, the coordinate will indicate the location of a hidden treasure.

Rules

You can reach the coordinates easily by traveling on public roads and land. The treasure is NOT hidden on private property. If your coordinates take you to private land (residential homes, businesses, commercial buildings, etc.) your solution(s) are incorrect.
Minimal effort is required to retrieve the treasure from its hiding place. You do not need to dig or move anything.
The first person (or team) to retrieve the treasure is the winner. Once the treasure is found, the contest is over.
The contest is brought to you by www.puzzlor.com. Contestants participate at their own risk. The author and www.puzzlor.com, Analytics magazine, INFORMS and Lionheart Publishing are not responsible for any injuries, damages or costs incurred while participating in this contest.
If you find the treasure, send an e-mail to This e-mail address is being protected from spambots. You need JavaScript enabled to view it indicating that you have found it so the puzzlor website can be updated.
Have fun and be safe!

Notes

A GPS enabled device will be helpful in leading you to the treasure’s coordinates.
The contest is active until someone correctly completes all of the puzzles and retrieves the treasure from its hiding space. Notification will occur on the puzzlor website (www.puzzlor.com) when someone has retrieved the treasure.
Additional questions can be sent to This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

John Toczek is the manager of Decision Support and Analytics for ARAMARK Corporation in the Global Risk Management group. He earned a bachelor’s degree in chemical engineering at Drexel University (1996) and a master’s degree in operations research from Virginia Commonwealth University (2005). He is an INFORMS member.