Ticket to Ride is a board game created by Alan R. Moon that has been growing in popularity since its first release in 2004 by Days of Wonder. The game components include a map with cities and defined train routes, sets of 45 colored, plastic train car tokens for up to five players, destination tickets, and colored train cards. The premise of the game involves collecting enough of the colored train cards to claim or build train routes to connect various major cities in the United States and southern Canada to earn points as well as completing routes designated on the destination tickets. The game itself is not only a fun way to spend hours playing but it is also a good tool to showcase various concepts in graph theory and combinatorics. Graph theory may also be useful in creating or enhancing game play strategies.
Set Up and Game Play
The original version of the game has a map of the United States and southern Canada with 30 destination tickets. An expansion to the original game features larger sized card sets as well as 39 additional destination tickets for what is referred to as the “Mega Game” variant. Throughout this analysis, I will assume all features of the “Mega Game” will be used unless otherwise stated. Since the first release, maps of Europe, Switzerland, Germany, Scandinavia, Asia, India, Africa, and the Netherlands have been added as well as a card game, a dice expansion, and additional destination ticket expansions have been created with the same basic game play. The original map is shown in Figure 1.The set up for the game begins with each player selecting his/her set of color train tokens. Next each player is dealt four of the colored train cards that players can later use to build or purchase train routes...
... middle of paper ...
...the game. Other plays could be going for the same tickets and routes or they could be attempting to block other players from completing a strategy. Graph theory can be used to help but does little to account for these unknowns. Even without a winning strategy, Ticket to Ride is a good medium to showcase different definitions and theorems within graph theory in accessible terms that can be understandable to more people while still being an enjoyable game to play.
Works Cited
Days of Wonder, "Game Rules - Ticket to Ride." Last modified 2013. Accessed November 29, 2013. http://cdn0.daysofwonder.com/tickettoride/en/img/tt_rules_2013_en.pdf.
Harris, John M., Jeffry L. Hirst, and Michael J. Mossinghoff. Combinatorics and Graph Theory. New York: Springer, 2008.
Rosen, Kenneth H. Discrete Mathematics and Its Applications. New York: McGraw Hill Higher Education, 2007.
Get an all-access rides bracelet or hand tickets over for the classic Merry-Go-Round, Tilt-A-Whirl, Triple Twist and the Super Shot.
Since the beginning of the United States the American people have been on the move. Public transportation has played a major role in the development of this nation and in bringing its citizens together. In the book “Divided Highways”, author Tom Lewis takes the reader on a journey of the building of the Interstates and the consequences(good and bad) that came from them. Lewis believes that the Interstates are a physical characteristic of America and that it shows “all our glory and our meanness; all our vision and our shortsightedness”(xiv).
Historically journeys were seen as the physical movement of a group of people migrating from one place to another. Additionally, journeys were usually only found throughout the history of civilization and religion. Despite this, journeys come in all aspects and are found in a variety of mediums. Specifically, two journeys that are found in the literary works of The Epic of Gilgamesh and Monkey: A Journey to the West are physical and intellectual. These two stories exemplify what a journey consists of by construction the plots around each protagonist participating in both journeys.
0.1 abstract In a graph theory the shortest path problem is nding a minimum path and distance between two vertices. The ap- plication in many areas of shortest path algorithms are such as geographical rout- ing, transportation, computer vision and VLSI design involve solving optimiza- tion problems on large planar graphs. To calculate the shortest path we need to know some algorithms like Kruskal's algorithm,Prim's algorithm,Dijkstra's algorithm,BellmanFord's algorithm.
Often, when people think of the functions of train, they simply view them as modes of transport. But, in literature, this does not appear to be the case, as trains can be used to create a means of escapism for the characters
Flashing orange text on the black screen of the overhead time chart is a reminder that my ride will arrive in precisely three minutes. The white letters on the train stop sign read "Neureut Kirchfeld", reminding me once more of where I am. I am an exchange student in Karlsruhe, a German city of over 300,000 residents. It is early July and I am on my way to school. My normal is about three thousand miles away, but my peace of mind and happiness are right in front of me in the form of yellow street cars zooming by, storks gliding through the milky blue sky, and the slow breeze of a summer morning.
The bus that took us to the Theme Park was huge, with room for a
From the dawn of time, man has followed his urge to travel; sometimes neglecting the enjoyment of the journey in pursuit of the destination. Although two of the favorable means of passenger transportation - the plane and the train - accomplish the task of arriving at a destination, there are distinct differences in their capacity for comfort, time, scenic value, and safety.
Who doesn’t love a train ride? It offers a unique experience that no other vehicle can match. In a previous issue, we covered the Trans-Siberian Railway. In this article, we will be going on a journey aboard the Bernina Express, beginning our journey from Chur in Switzerland, traveling through wild Canton of Graubünden to Mediterranean Tirano in Italy.
Public transportation is an essential part of a city. A good public transit can encourage a city’s economic activities and can provide its citizen a convenient life. Does our Phoenix public transit work well? Does it provide sufficient service to the citizen? From my experience, the answer is no. This November I tried to attend the popular State Fair in Phoenix. However, I found that there were not any buses or metros could take me to the fair directly. It means I need 2 hours or more spend on the public transits. As the sixth most populous city nationwide (“Phoenix Quick Fact” 1), compared with Los Angeles and other big cities in America, Phoenix’s public transportation is indeed subpar. Due to Los Angeles has 154 bus lines and 30 metros (“Schedule”), New York has 316 bus lines and 28 subways(“Maps & Timetables”), while Phoenix only has 98 bus lines, and the number of metro line is only one! (“Route Schedules & Maps”) The problem is
Most people take the urban public transportation system for granted. It is used in every aspect of our daily lives: work, education, medical necessities, recreation, etc. It is also important for the transportation of goods and services, which aids the growth and maintenance of our economy. Urban public transportation is the critical component of our quality of life and economic stability. The MBTA, the Massachusetts Bay Transportation Authority, is Boston and Eastern Massachusetts’s major transportation service. The MBTA has played a central role in the development of Boston and surrounding cities and towns for more than a century; providing service from 175 cities and towns into Boston. On an average weekday over 1.2 million trips are made on the subway, buses, commuter lines and other services in the mass transit system. With an international airport, a ship port, the highways, and the rail lines to connect regional cities and towns to national and international destinations and markets, Boston’s urban public transportation system has made the region’s growing role in the global economy possible.
If you already know what a binary tree is, but not a general tree, then pay close attention, because binary trees are not just the special case of general trees with degree two. I use the definition of a tree from the textbook, but bear in mind that other definitions are possible.
My first experience with a carnival ride was a Ferris wheel at a local fair. Looking at that looming monstrosity spinning the life out of its sardine-caged occupants, I was dumbstruck. It was huge, smoky, noisy and not a little intimidating. Ever since that initial impression became fossilized in my imagination many years ago, these rides have reminded me of mythical beasts, amazing dinosaurs carrying off their screaming passengers like sacrificial virgins. Even the droning sound of their engines brings to mind the great roar of a fire-breathing dragon with smoke spewing from its exhaust-pipe nostrils.
Social Network theory dates back to the 1950’s where Barnes (1954) is credited with coining the term. Social Network Theory is the study of how the social structure around a person, group, or organization affect beliefs or behaviors (Dunn, 1983) The theory views relationships in terms of nodes and ties. Nodes can be defined as individual actors within networks, while ties are the relationships between the actors. (Dunn, 1983). These nodes and ties are often displayed in a diagram which shows the connection between them. Unlike traditional sociological studies, Social Network Theory does not assume that it is the attributes of individual actors, but rather the attributes of the individual are less important, but rather the relationships and ties with other actors within the network is what is important.
This report illustrates the results and discussion of the Travelling Salesperson Problem (TSP). The travelling Salesperson travels from University Of Pretoria (UP) and has to travel to four possible locations using the shortest path. BFS and DFS will be used and compared according to efficiency of each for the Salesperson to reach his goal in the most optimal manner. The goal-state allows the Salesperson to visit all of the locations below and return to UP with the most optimal path. The following locations have to be visited: