Ten Years in the Making: the Four-Park Challenge

In lieu of posting a summary of Day 21 today, we're going to postpone that until we get back to South Carolina. Today was a great day and we want to share the details, particularly about our students' projects and final presentations, but we need to pack and hit the road bright and early tomorrow morning. Stay tuned for a few more blog posts over the coming days. In the mean time, we'll share some details about the Four-Park Challenge we ran with alumni last week!

One of my favorite movies when I (Dr. Hutson) was young was called Midnight Madness. The movie centered on a scavenger hunt designed by a brilliant graduate student in which undergraduates race around Los Angeles collecting clues to find more clues. Each new clue offered a direction for the next, challenging the students to decipher clues from physics to music. The movie starred a really young Michael J. Fox (then Michael Fox) as an angsty young teenager who desperately wants the attention of his older brother, who is mostly interested in the scavenger hunt and the affection of his girlfriend. Michael J. Fox’s character softens his angst and helps his brother’s team win the race by a matter of seconds. The movie appealed to me as a kid because I loved solving puzzles and racing competitions, and I ended up creating wild-goose chase games for my friends to solve. Given the enduring popularity of shows like The Amazing Race, it seems that this type of competition appeals to many.  

One of the fundamental problems in the area of combinatorial optimization is the Knapsack Problem. Like many problems in this field, it is easy to state but difficult to solve. Suppose you have many items that you would like to take on vacation, and each has some value to you on the trip. However, each also has some capacity that it takes up in your suitcase. The problem then is to maximize the value of the items taken while not exceeding the capacity limitations of the suitcase.

This year, Math and the Mouse (MatM) celebrates its ten-year anniversary, and we invited our alumni to come back to share their life experiences since their MatM trip and to participate in a Knapsack/Amazing Race Competition that we called The Four-Park Challenge. Four alumni returned to take part in the competition, Joey Ianetta ‘15 (MatM ’14), Courtney Brown ‘20 (MatM ’18), and Kyle Gartman ’21 and Hannah Thomas ‘22 (both MatM ’19). The alumni and their friends made up three teams added to six teams from this year. Five of this year’s teams were composed of students, and one team was comprised of the professors accompanied by special guests, Furman President Elizabeth Davis and her husband, Charles!

Game Preparation

The professors worked with Len Testa of Touring Plans, whom you met earlier in the blog, to create a point value for each attraction (rides, shows, and character meet and greets) in all four Walt Disney World theme parks. This point value was based on average wait time for the attraction, ride duration, and a measure of how often the attraction breaks down. For example, Slinky Dog Dash in Hollywood Studios has an average expected wait time of 90 minutes/day (two standard deviations above average), a ride duration of 3 minutes, and an average downtime of 65 minutes/day (1.5 standard deviations above average). We used these “z-scores” for all rides to give them point values. Slinky Dog, for example, got an overall point score of 700, the highest among all of the rides over the four parks. The challenge was for each team to accumulate as many points as possible within the time constraint of seven hours (8:00am-3:00pm). That is, in the language of a Knapsack Problem, how many rides (items to take on vacation) could be fit into the time constraint (suitcase) to maximize the points (utility value)? There were also bonus points for completing special challenges like completing ten attractions in a single park, visiting an attraction (ride, show, or meet) in each park, meeting the Fab Five characters (Mickey, Minnie, Donald, Goofy, and Pluto), and taking different modes of transportation between parks.

The Math Behind the Scenes

After an initial meeting on Thursday to explain the rules, teams were dispersed to strategize and propose a plan for tackling the challenge. The Knapsack Problem is known to be NP-hard. This means that although producing a good solution might be easy and quick, verifying that is optimal is extremely difficult because it basically requires one to enumerate all possible solutions (which could be exponential in size).  So, most people use heuristic algorithms to produce near-optimal solutions in quick fashion to solve these types of problems. One of the most commonly used algorithms for the Knapsack Problem is known as the Bang-for-the-Buck Algorithm. This algorithm makes selections based on which attractions produces the most points per amount of time (wait time plus ride duration) it takes to achieve the points. In looking over the solutions, many teams employed this strategy, especially early in the day. Many teams chose ride Space Mountain (510 points) early, giving them a small wait (5-10 minutes) and lower ride duration (3 minutes).  This equates to achieving around 60 points per minute of wait. Contrast this with teams that rode “it’s a Small World” (230 points) early in the day, which had a small wait time (5-10 minutes) but has a 14-minute duration. This equates to only achieving around 10 points per minute. Teams that employed the Bang-for-the-Buck algorithm repeatedly throughout the day generally were able to accumulate more points, while those that chose to get in line for high point rides like Rise of the Resistance (620 points) in the middle of the day and waited more than an hour, reduced their points per minute to around ten (even lower if you factor in time to get to the ride).  

Bonus Effects

A strategy that paid off for most teams was to earn bonus points (1500) by not purchasing Genie+ or Lightning Lanes for the competition. Only two teams purchased Genie+, one alumni team and the “Profs and Prez” team. It turned out that these two teams were not able to make up for the lack of bonus points through lowering their wait time. Popular rides have Lightning Lane availability that fills up very quickly, and this pushed the available Lightning Lane time passed the 3:00 finish mark and forced Lightning Lane selections for smaller rides which did not have long wait times during the morning hours of the competition and had smaller point values reducing the bang for the buck. However, the teams that got Genie+ service generally felt not-so-bad at the end of the day because they didn’t have to wait in line all day.

Almost all teams achieved the bonus of riding ten rides in one park. Since the Magic Kingdom opened an hour earlier than other parks, and it has an abundance of attractions, most teams were able to achieve ten rides in that park within the first two-and-a-half hours and move on to another park. This bonus of 1000 points was neutralized since all but one team satisfied the requirement.  

And Now For What We’ve All Been Waiting (In Line) For

First place team: Jacob, Erin, Katie, and Riley

The winning team was a student team comprised of Jacob, Erin, Katie, and Riley. The bonus point structure did benefit teams unequally, and the winning team took full advantage of it, amassing 3700 points by riding ten rides in the Magic Kingdom, riding a ride in each of the four parks, taking four different modes of transportation, and doing this without purchasing Lightning Lanes. That was pretty impressive, and it separated them from the second-place team. The winning team rode 16 rides, visited four parks, and accumulated 7830 points by riding eleven Magic Kingdom rides, two rides in Animal Kingdom, two rides in Epcot, and one ride in Hollywood Studios. Their ride total was 4130 points. 

Meanwhile, the second-place team (Will, Hayes, and Ellis) hustled all day but only got 2700 bonus points because they didn’t make it to all four parks. However, they achieved more ride points (4565) than the first-place team by riding popular rides in Magic Kingdom and Epcot.  

Second place team: Will, Hayes, and Ellis 

The third-place team had the most diverse set of attractions visited by riding only ten rides in the Magic Kingdom and Epcot but meeting all Fab Five characters. They had 3500 bonus points and 3200 ride points to achieve 6700 total points. 

Third place team: Alyssa, Emily, Morgan, and Hannah

Our highest alumni group was Hannah and Kyle. They only rode 11 rides, but hit pretty much all of the popular rides in Magic Kingdom (Seven Dwarfs Mine Train, Space Mountain, TRON: Lightcycle Run, Peter Pan’s Flight, etc.) and one ride (Tower of Terror) in Hollywood Studios. Their 3960 ride points combined with 2500 bonus points to finish fourth. 

Fourth place: Hannah '22 and Kyle '21 

The cumulative total for each team is shown in the table below.

The Profs and Prez team

Mathletes stretching after the Four-Park Challenge

Meanwhile, the Profs and Prez team achieved sixth place but were one of only two teams to make it to all four parks. Their ride total was 3800 but only achieved 2100 bonus points, limited by their purchase of Genie+. However, kudos to President and Dr. Davis for walking over 20,000 steps, surviving the Tower of Terror, taking tons of pictures on the safari, getting stuck on the Navi River journey for twenty minutes listening to a song that rivals “it’s a small world”, and doing that with huge smiles on their faces. We enjoyed spending the day with them, laughing, and exploring the parks.  We may not have won the race, but we didn’t wake up the next day complaining about how sore we were like some twenty-year-olds that we know.

The After Party

After the long day, we spent the evening celebrating at Splitsville. Our alumni gave advice to our class on what matters after Furman. Each spoke to the impact of their Math and the Mouse time and other experiences they took advantage of while at Furman had on their lives today. It was fun to see how The Furman Advantage has paid off for these alumni, and we can’t thank them enough for coming back and interacting with our students. We also want to give a huge thank you to Mark and Melissa Gibson, Furman parents and owners of Splitsville, for hosting us for the event. Their hospitality was without bounds, and our students could not stop raving about the experience. The great food, bowling, and conversation complemented the fantastic second floor viewing of the inaugural drone show at Disney Springs.  

Gratitude

Through the decade since our first iteration of Math and the Mouse, we have been so lucky to work with amazing students, both during the three-week May Experience term in Florida as well as in other settings beyond a traditional classroom. When we planned the Four-Park Challenge, we reached out to our MatM alumni to see if they would consider supporting Math and the Mouse on Dins Day, Furman’s annual day of giving held on the last day of classes, even if they weren’t able to travel to Florida to interact with our students directly. We issued a challenge to our alumni that was tied to the Four-Park Challenge. For each donation received that ended in a 0, that would contribute bonus points towards the professor team’s score whereas donations that ended in a 5 would deduct bonus point from the professor team’s score, ultimately boosting the non-faculty teams. During the event at Splitsville, we shared that through the generosity of our MatM alumni and the Furman family, the professor team had 15 more donations supporting them than the students. We translated this difference into 1500 bonus points for the Profs and Prez team, which bumped us up from 6th to 2nd place! All silliness aside, we are so thankful to get to work with amazing students during their time at Furman and keep in touch with them afterwards, but we are also extremely grateful for the support of the past decade from friends, family, and Furman.