Question 1: Starcraft 2 Build Order Optimizer 200

Question 1: Starcraft 2 Build Order Optimizer 200

The Operations Research Challenge 2012 Team Number: Question 1: Starcraft 2 Build Order Optimizer [200] In the game of Starcraft, you are given control over an alien race and must lead them to victory against an opposing player’s aliens. You will be given control of the Protoss race and must make the best decisions to beat your opponent. There are three fundamental aspects you can develop in the game of Starcraft: economy, army and technology. However, you are limited in how quickly you can develop the three aspects since improving any one of these three areas requires resources. The resources you have are food, minerals and gas.

For this problem, you must decide what to build and when to build it in order to reach a milestone in the fastest time. Table 1 shows the buildings available to you, the cost of making the building, the time required to complete construction, and the building you already need to have constructed in order to build this building. Building Minerals Gas Time (s) Pre-requisite Nexus 600 0 100 None Pylon 150 0 25 None Assimilator 110 0 30 None Gateway 225 0 65 Pylon Cybernetics Core 225 0 50 Gateway Robotics Facility 300 150 65 Cybernetics Core Table 1: Buildings you have access to and their requirements Table 2 shows the units you can build, their cost, time to build and the building that must be used to build the unit.

When building a unit, the building will be busy and cannot do anything else or build any other units. For example, if you are building a zealot from the gateway, you cannot build any other unit (zealot, stalker or sentry) from that gateway until the zealot is completed. In order for you to build two zealots, stalkers, sentries or a combination of any of these two at the same time, you must have already completed building two gateways. 1

The Operations Research Challenge 2012 Team Number: Furthermore, each unit requires food. If your army does not have a sufficient amount of food, you cannot start building the unit. Food is crucial in keeping your army strong and alive. Details on how food works will be provided later. For now, it is sufficient to understand that each unit requires a different amount of food specified in Table 2 below. Unit Minerals Gas Time(s) Building Food Req. Probe 75 0 17 Nexus 1 Zealot 150 0 38 Gateway 2 Stalker 175 75 42 Gateway* 2 Sentry 75 150 37 Gateway* 2 Immortal 400 150 50 Robotics Facility 4 Table 2: Units you have access to and their requirements *Stalkers and Sentries can’t be built from a Gateway until a Cybernetics Core is built.

You start the game with 1 Nexus, 6 probes, and 75 minerals. You can make use of probes to mine for minerals at a rate of 1 mineral/second. Thus, when you start the game, your six probes will give you 6 minerals/second. You can continue to build probes from your Nexus to improve your economy. However, a single Nexus can only support a maximum of 24 probes mining minerals. If there is a 25th probe trying to mine extra minerals, that probe becomes useless. If you wish to mine for minerals with more than 25 probes, you must build a second Nexus to support these extra probes.

In order for you to obtain gas, you must build an Assimilator. Once you have an Assimilator built, you can start to mine gas at a rate of 1 gas/second. However, the Assimilator can only support a maximum of 3 probes. Furthermore, you can only build a maximum of 2 Assimilators for each Nexus you own. That is, if you have 1 Nexus, you can have 2 Assimilators. If you have 2 Nexus, you can have 4 Assimilators. The probes mining gas will not affect the maximum of 24 probes mining minerals on a Nexus. Therefore, each Nexus can support a maximum of 30 probes – 24 mining minerals and 6 mining gas (2 Assimilators).

When an Assimilator is completed, make sure to state how many probes you want to assign the task of mining gas. If none is stated, it will be assumed that you do not get any gas.

During the course of the game, you will also want to make sure that you are not focusing too much on economy (mining minerals and gas). You will have to ensure that you have enough of an army to fend off any attacks your opponent may make. The zealot, stalker, sentry and immortal units are your army units. These units can fight for you when the enemy comes to attack your base. Specific milestones are stated below: you must ensure that you have a sufficient army for potential attacks at specific times. How we know if your army is sufficiently large is based on the food requirements. Therefore, if the size requirement is 4, you must have at least two of any of the following units – zealots, stalkers and sentries.

You can also meet the 2

The Operations Research Challenge 2012 Team Number: 4-army size requirement by having just an immortal. Any mixture of units will be sufficient, as long as the food requirements are greater than or equal to the size requirements. Note that probes do not count towards your army size. Army Size Constraints (You must have:) ● 4 food worth of army at 270 seconds ● 10 food worth of army at 500 seconds Food requirements also have another property that must be considered. As mentioned earlier, your units require various proportions of food to function. If you do not have the sufficient amount of food, you cannot build that unit.

A Nexus is a source of food and can support a total of 10 food. A pylon also supplies food for your units and can support a total of 8 food. Since you start with a Nexus, you can have up to 10 food worth of units before you must either build another Nexus or pylon. Since you start with 6 probes (a total of 6 food requirements), you can build at most another 4 probes (6+4 = 10) before you must build a new Nexus or pylon to continue building units.

The final aspect of the game is technology. We can increase our economy by building probes, Nexus and Assimilators. Army can grow by building fighting units. Technology will give you access to stronger and better units. The immortal is considered a “tech” unit since it is much stronger than the zealot, sentry and stalker. However, to obtain an immortal, we must spend more time getting the advanced building, the Robotics Facility. A common tactic in Starcraft is to use a timing push. A timing push occurs when a player obtains a specific technology and sufficient army size to attack their opponent.

In our case, the technology we want is in the immortal unit and once we have this new technology, we know our army is much stronger. Of course, we will need an army to help strengthen our immortal further as well.

The main goal of this problem is to build 2 Immortals, 4 sentries, 6 stalkers and 8 Zealots in the fastest possible time. Once we have these units, we can attack the enemy. However, time is very important. The longer we delay, the more time we give our opponent to build up his own army to defend our attack. The points you obtain will be based on how fast you can get the army required for this attack. The faster you are able to get these units, the more points you will get. However, you must ensure that you meet the Army Size Requirements. If you are not able to meet the size requirements, your time will be incremented by 30 seconds/food deficit.

Therefore, if at 500 seconds you only have 6 food worth of army, 120 seconds will be added to your final time. When answering this question, it is best for you to make a point form list of what you will do and at what time.

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The Operations Research Challenge 2012 Team Number: Therefore, an example answer can be @ start, time 0 Minerals: 75 Gas: 0 Food: 6/10 @ time 0, build a probe Minerals: 0 Gas: 0 Food: 7/10 @ time 17, probe completes Minerals: 102 Gas: 0 Food: 7/10 @ time 50, build a pylon Minerals: 183 Gas: 0 Food: 7/10 @ time 75, pylon completes Minerals: 358 Gas: 0 Food: 7/18 @ time 100, build a gateway Minerals: 308 Gas: 0 Food: 7/18 @ time 100, build a probe Minerals: 233 Gas: 0 Food 8/18 @ time 117, probe completes Minerals: 352 Gas: 0 Food 8/18 @ time 165, build a zealot Minerals: 586 Gas: 0 Food 10/18 @ time 167, build a Nexus Minerals: 2 Gas: 0 Food 10/18 @ time 203, zealot completes Minerals: 306 Gas: 0 Food 10/18 ….

Make sure that you have enough resources to build what you want at the time you have specified. If you do not have sufficient resources, you will be penalized. 4

The Operations Research Challenge 2012 Team Number: Question 2: London Olympics [40] The London Olympics start on 2012-7-27. In order to represent your country, you must solve the following puzzle: O L Y M P I C - L O N D O N 2 0 1 2 7 2 7 Each letter represents a single digit number between 0-9, inclusive. The digits assigned to the letters have to all be different. For example, assigning 7 to both M and Y is not allowed.

Please help our national athletes by informing them whether this puzzle a. Has only one solution (if so, please state the solution). b. Has multiple solutions (if so, please state at least two solutions). c. Does not have a solution (if so, please provide an explanation of why there can be no solution).

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The Operations Research Challenge 2012 Team Number: Question 3: Planning a Picnic [60] Having participated in TORCH 2012, you have been assigned the task of making five picnic tables for an upcoming family get-together. Each picnic table has four legs (at 3 ft. high), requires five support beams (at 4 ft. long), and has a table top made of six, 5 ft. long boards. You can purchase only wood planks that are 14 ft. long. All table components have to be one continuous piece. One solution is to buy 30 wood planks and to cut each with a pattern as shown in Table 3.

The pattern indicates that each wood plank is cut into one piece of 3 ft., one piece of 4 ft, one piece of 5 ft., and with 2 ft. left over. Having 30 wood planks cut with the pattern in Table 3, you will have 30 legs, 30 supports and 30 long boards. Therefore, you have enough legs, supports and long boards to make five picnic tables. However, as an expert in Operations Research, you need to find the minimum number of wood planks in order to make five tables. You also need to state the pattern(s) used to cut each plank.

Cutting Pattern 3 ft. 4 ft. 5 ft. 1 1 1 Table 3: A cutting pattern 6

The Operations Research Challenge 2012 Team Number: Question 4: A Winning TORCH Strategy [100] It is the night before the third annual TORCH contest, and as team captain you want to maximize your chances of winning the next day. To do so, you will need to decide how you should prepare beforehand, what you should bring and the strategy your team should use during the day. You will have two other team members to direct, and you must provide a description of what all three teammates should do.

Each student on the team can bring either a set of reference books with them, or any two of the following (two of the same item is allowed):  A calculator  Pencils for everyone  Paper for the team to use  A can of Red Bull to stay awake As well as bringing items, each student can also choose how to prepare for the quiz the night before by doing only ONE of the following:  Reading reference books  Reading Wikipedia  Sleeping During the quiz there are two phases: morning and afternoon. For a particular phase, you must decide what each of the three members will do (they can only do one per phase):  Sleep  Ask questions  Answer questions When making your choices as team captain, there are a number of rules you must follow to select what a member should do to prepare, bring and do for the contest.

These are the rules you must follow:  Each person can bring no more than two items.  If they bring reference books then they cannot bring anything else.  At least one person needs to bring pencils.

 At least one person needs to bring paper.  Each person can do only one of the three preparations.  A member can use reference books only if they studied reference books the night before, but the person using the books does not have to be the one to bring them.  Only one person can use a set of reference books at a time. 7

The Operations Research Challenge 2012 Team Number:  A member can do only one action in each phase (morning and afternoon).  Only one member can use a can of Red Bull, but a team may bring (and use) multiple cans.  If a member sleeps (either the night before or during the contest) then they are considered rested for the remainder of the contest.

They are also considered rested if they drink a Red Bull. Drinking a can does not require an action, but occurs at the start of a phase and only lasts for the phase it is used in. For example, Person #2 drinking a can in the morning phase means they are rested for the morning phase, but not rested in the afternoon phase.

 A member can answer questions only if they are rested. The success of a team is measured by their TORCH Points (TPs). How does a team get TPs? By preparing and competing as efficiently as possible, of course. Specifically, these are the ways to gain TPs for a team:  (5 TP) Awarded for every calculator a team has.  (15 TP) Awarded for asking questions  (20 TP) Awarded for answering questions without a reference book  (22 TP) Awarded for asking questions with wiki knowledge  (25 TP) Awarded for answering questions with a reference book Format for your answer: For this question, you must provide a plan for the three team members, including: how they should prepare, what they should bring and what they will do in the morning / afternoon phases.

An example solution: / 1: Sleep / Calculator, Red Bull / Answer / Answer 2: Sleep / Pencils, Paper / Answer / Answer 3: Read Wiki / Calculator, Calculator / Ask / (drink) Answer Score = (Answer without books * 5) + (Calculators * 3) + (Ask with wiki * 1) Score = (20 * 5) + (5 * 3) + (22 * 1) Score = 137TP 8

The Operations Research Challenge 2012 Team Number: Question 5: March Madness - Sweet Sixteen [200] March Madness is the top US college basketball competition where more than 60 top teams around the nation compete for National glory. After two rounds of the competition, sixteen teams are left in the tournament. The remaining sixteen teams, known as the Sweet Sixteen, are placed in a draw (see attached) where only the winner can advance and the losers go home. NCAA, the organizers of March Madness, would like you to help their ticket department for the remaining games. Given the demand for tickets to the games, the March Madness organizers want you to design a ticket package to maximize their profits.

There are two types of tickets: Team Pass tickets and Individual Game tickets. The holder of the Team Pass ticket may attend all games played by a specific team. However, the Team Pass tickets must be purchased before the start of Sweet Sixteen. In comparison, the Individual Game tickets are sold before each game and they are valid for that game only. The prices of the Team Pass ticket for each team are listed below in Table 4. The prices of the Individual Game tickets are listed in the attached “2012 March Madness Tournament Bracket”. West South Michigan State $40 Game 1 Kentucky $60 Game 3 Louisville $20 Indiana $50 Missouri $20 Game 2 Duke $80 Game 4 Marquette $40 Baylor $20 East Mid-West Syracuse $50 Game 5 North Carolina $70 Game 7 Wisconsin $30 Michigan $20 Ohio State $40 Game 6 Kansas $60 Game 8 Florida State $30 Georgetown $20 Table 4: Team Pass ticket prices The capacity for each game is 10,000 and individual tickets are sold only if capacity is not met.

If the number of Team Pass tickets sold to the two competing teams exceeds the capacity, a refund must be paid to all holders of the Team Pass tickets who cannot attend the game due to capacity. The refund is twice the price of the Individual Game ticket. The holders of the Team Pass ticket are still eligible for the next game if their team has advanced. Your job is to determine: ● The number of Team Pass tickets to be sold for each team in the Sweet Sixteen in order to maximize profit.

Furthermore, you may ask an expert for a prediction of the outcome of three specific games. The expert will inform you about the teams playing in the game and the outcome. The expert’s prediction is 100% correct. 9

$10 $20 $30 Game #:1 Michigan State Game #:1 Louisville Game #: 9 Game #:2 Missouri Game #:2 Marquette Game #: 9 Game #: 13 Game #:3 Kentucky Game #:3 Indiana Game #: 10 Game #:4 Duke Game #:4 Baylor Game #: 10 Game #: 13 Game #:5 Syracuse Game #:5 Wisconsin Game #: 11 Game #:6 Ohio State Game #:6 Florida State Game #: 11 Game #: 14 Game #:7 North Carolina Game #:7 Michigan Game #: 12 Game #:8 Kansas Game #:8 Georgetown Game #: 12 Game #: 14 Game #: 15 Game #: 15 $10 $10 $10 $10 $10 $10 $10 $20 $20 $30 $20 $40 2012 March Madness Tournament Bracket

The Operations Research Challenge 2012 Team Number: Question 6 (a): Finding a Cure [100] Meningitis Ischemia Syndrome (MIS) is a disease where an inflation of the brain is caused by deficiency of blood supply. A group of scientists have identified one hundred core chemicals that may help cure MIS, a highly contagious disease. The scientists have collectively discovered that the cause for MIS is through the infection of a chemical solution. The solution, known as the MIS-Composition or MISC, is composed of one or more core chemicals. MISC has the following properties: 1. The MISC will turn healthy living cells into infected cells.

2. The combination of MISC with other core chemicals will also turn a healthy cell into an infected cell.

3. Any combination of core chemicals that does not include the entire MISC chemicals will instantly kill a living cell. 4. The number of chemicals in MISC is at least two and at most ten. The scientists hypothesized that once the composition of MISC is known, a cure may be found. The objective of the scientists is to determine the core chemicals in MISC by making chemical solutions and testing them on cells. But first, they need your help to determine the minimum number of living cells required to fully identify MISC. Your job is to figure out that number. Please also describe your testing strategy.

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The Operations Research Challenge 2012 Team Number: Question 6 (b): Transporting the Cure [100] Once the composition of MISC is known, the cure is created and stored in cells for transportation. We are given a container with a fixed-size grid of cells. Each position of the grid contains a cell in one of two possible states, alive or dead. Every cell interacts with the neighbours around it. At each step in time, the following transitions occur: 1. Any live cell with fewer than two live neighbours dies, as if caused by under-population. 2. Any live cell with two or three live neighbours lives on to the next generation.

3. Any live cell with more than three live neighbours dies, as if by overcrowding. 4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

Given the grid below and the set of rules above, the problem is how to place the maximum number of live cells on the grid container so that this number will not change over time (no cell dies or is created - the cell grid remains static). Here is an example of a smaller container that worked in the previous transportation, where each live cell is indicated by an “X”: X X X X 11

The Operations Research Challenge 2012 Team Number: Question 7: London Tube [200] You are staying at The Savoy hotel in London for 14 days during the Olympics. You want to see 28 sports (i.e., all sports specified in Table 5 below).

Being an operations research specialist, it should be no problem for you to save time by travelling between different event venues by subway. The sports you want to see are located in seven different venues, each of which can be reached by subway from your hotel. The hotel is located at the Charing Cross station. The closest station(s) to each venue are indicated in Table 5. If there are two stations indicated, either of them can be used to reach the venue.

One visit to a particular venue allows you to view one sport (even if it is a venue for multiple sports). Every venue can be visited at most once per day. For example, you cannot see both boxing and fencing at the ExCeL centre on the same day. You are allowed to see at most two events per day. All events at a given venue start and end on the days specified in the Table 5 below. This means that you can view the sports in that venue only between the given start day and end day, inclusive. For example, football can be viewed on days 1, 2, 3, 4, 5, 6, 7 only. A map of the London Tube (subway), which indicates the locations of the seven venues is attached.

You want to minimize the total travel time subject to the above constraints. The time of traveling between two stations on the same subway line is 1 minute, and the required time for switching subway lines is 3 minutes. The travel time between two venues located at the same subway station is 0. You need to return to the hotel, whose location is also indicated on the map, at the end of each day. Therefore, you need to indicate the subway path you take each day, the venues you visit, the sports you watch on each visit, the total travel time for each day and the total travel time over the 14 days.

The attached map has a legend indicating the names of the subway lines. Circles on the map indicate interchange stations. For example, Charing Cross is an interchange station between Bakerloo Line and Northern Line, while the Embankment station is an interchange station between Northern, Bakerloo, Circle and District Lines. Non-interchange stations are indicated by small rectangles, see, for example, the Temple station just to the right of Embankment. Temple is a non-interchange station on the Circle Line and also a non-interchange station on the District Line.

In writing your answers, please indicate the name of the subway line if there is any ambiguity (e.g., if the station is an interchange station or if there are two stations with the same name on different lines).

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The Operations Research Challenge 2012 Team Number: Example of time calculations based on the subway map: Suppose you want to get to Baker Street station on the Metropolitan Line from your hotel at Charing Cross. One way to do so is to go through 4 stations (Piccadilly Circus, Oxford Circus, Regent’s Park, Baker Street on Bakerloo Line) and then switch stations to get to Baker Street station on Metropolitan Line. The total travel time is the 4 minutes on the Bakerloo Line plus 3 minutes for switching lines at the end, so 7 minutes. If you then want to get to West Hampstead on the Jubilee Line, you could travel from Baker Street to Finchley Road on the Metropolitan Line (1 minute), switch to Jubilee Line (3 minutes) and then travel to West Hampstead on the Jubilee Line (1 minute).

Thus, the total travel time from Baker Street on the Metropolitan Line to West Hampstead on the Jubilee Line is 5 minutes. The total travel time from your hotel to West Hampstead using this route is 12.

Format for your answer: Day 1: subway path: Charing Cross, Piccadilly Circus, Oxford Circus, Regent’s Park, Baker Street on Bakerloo Line, Baker Street on Jubilee Line, St. John’s Wood total travel time = 8 minutes venue visited: Lord’s Cricket Ground sports watched: Archery subway path back to hotel: St. John’s Wood, Baker Street on Jubilee Line, Bond Street on Jubilee Line, Green Park on Jubilee Line, Green Park on Piccadilly Line, Piccadilly Circus on Piccadilly Line, Piccadilly Circus on Bakerloo Line, Charing Cross on Bakerloo Line total travel time = 11 minutes Day 1 total travel time = 19 minutes Day 2: ...

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The Operations Research Challenge 2012 Team Number: Venue Closest station(s) (subway line names) Start day End day Sports VeloPark Stratford (Central/Jubilee/DLR/ National Rail/ London Overground), West Ham (Jubilee/ District/ Hammersmith & City) 1 3 Cycling – BMX, Cycling – Track Wembley Stadium, Wembley Arena Wembley Park (Metropolitan/Jubile e Line) 1 7 Football, Rhythmic Gymnastics Greenwich Park Greenwich (DLR/National Rail), Cutty Sark (DLR) 1 8 Equestrian – Jumping, Equestrian – Dressage, Equestrian – Eventing, Paralympic Equestrian, Modern Pentathlon Basketball Arena Stratford (Central/Jubilee/DLR/ National Rail/ London Overground), West Ham (Jubilee/ District/ Hammersmith & City) 3 5 Basketball, Paralympic Basketball, Handball Aquatics Centre Stratford (Central/Jubilee/ DLR/National Rail/ London Overground), West Ham (Jubilee/ District/Hammersmit h & City) 5 14 Diving, Swimming, Synchronised Swimming, Modern Pentathlon – Swimming, Paralympic Swimming, Water Polo ExCeL Prince Regent (DLR), Custom House (DLR) 3 14 Boxing, Fencing, Judo, Table Tennis, Taekwondo, Weightlifting, Wrestling, Paralympic Table Tennis, Paralympic Judo Earl’s Court Earl’s Court (District/Piccadilly) 9 11 Volleyball Table 5: Venues, subway stations and time windows for different sports.

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For a large format version of this map see london2012.com/publications Transport for London Version A TfL 12.09 Reg. user No. 09/E/1621/P Correct at time of going to print River Thames River Thames 09/E/1621/P Harringay Green Lanes Northern Metropolitan Victoria District Circle Central Bakerloo DLR London Overground Piccadilly Waterloo & City Jubilee Hammersmith & City National Rail Riverboat services Interchange stations Tramlink Airport Station closed Blackfriars Step-free access from the platform to the street London Overground under construction MAYOR OF LONDON Transport for London Bermondsey Southwark Eastcote North Harrow Northwood Hills Northwood Moor Park Queen’s Park Kensal Green Neasden Dollis Hill Willesden Green Kilburn West Hampstead Swiss Cottage St.

John’s Wood Finchley Road Amersham Ruislip Manor Chorleywood Rickmansworth Watford Croxley Harrow- on-the-Hill Preston Road Hillingdon Ruislip Rayners Lane West Harrow Northwick Park Wembley Park Ealing Common Ealing Broadway Great Portland Street Baker Street Moorgate Aldgate Euston Square Acton Town West Acton East Acton Stamford Brook Ravenscourt Park Hammersmith West Kensington West Brompton Parsons Green Wimbledon Park Southfields East Putney Putney Bridge Wimbledon Victoria South Kensington Gloucester Road Embankment Blackfriars Mansion House Temple Cannon Street Bank Monument Barons Court Fenchurch Street Tower Hill Aldgate East Stepney Green Mile End Bow Road Bow Church Bromley- by-Bow Plaistow Upton Park East Ham Becontree Dagenham Heathway Elm Park Upney Dagenham East Upminster Bridge Hornchurch Upminster High Street Kensington Notting Hill Gate Bayswater Kensal Rise Brondesbury Caledonian Road & Barnsbury Edgware Road Edgware Road St.

James’s Park Sloane Square Westminster Barking Latimer Road Ladbroke Grove Westbourne Park Finchley Road & Frognal Royal Oak Goldhawk Road Wood Lane West Ruislip Greenford South Ruislip Hanger Lane Perivale White City North Acton Kilburn High Road South Hampstead Paddington Chancery Lane Bethnal Green Bond Street Oxford Circus Tottenham Court Road St. Paul’s Marble Arch Queensway Holland Park Lancaster Gate South Tottenham Leyton Midland Road Stratford Wanstead Park Leyton Leytonstone Snaresbrook South Woodford Epping Theydon Bois Debden Loughton Buckhurst Hill Redbridge Chigwell Roding Valley Fairlop Barkingside Newbury Park Wanstead Gants Hill Knightsbridge Hyde Park Corner Green Park Piccadilly Circus Leicester Square Russell Square Caledonian Road Hackney Wick Holloway Road Crouch Hill Arsenal Manor House Turnpike Lane Wood Green Bounds Green Arnos Grove Southgate Cockfosters Uxbridge Ickenham Waterloo Colliers Wood Morden South Wimbledon Tooting Bec Clapham South Oval Balham Clapham Common Tooting Broadway Stockwell Kennington Borough Old Street Angel Goodge Street Euston Mornington Crescent Camden Town Chalk Farm Regent’s Park Belsize Park Hampstead Heath Canonbury Gospel Oak Hackney Central Dalston Kingsland Homerton Kentish Town West Camden Road Upper Holloway Kentish Town Canada Water Canary Wharf Elverson Road Deptford Bridge Stanmore Canons Park Queensbury Watford High Street Kingsbury South Kenton Kenton North Wembley Wembley Central Stonebridge Park Harlesden Willesden Junction Kilburn Park Maida Vale Warwick Avenue Brondesbury Park Marylebone Lambeth North Elephant & Castle Charing Cross Blackhorse Road Seven Sisters Walthamstow Central Tottenham Hale Finsbury Park Highbury & Islington Pimlico Brixton Wapping New Cross Vauxhall Limehouse Westferry Devons Road Pudding Mill Lane West India Quay Cutty Sark for Maritime Greenwich Greenwich Lewisham Blackwall East India West Ham Warren Street All Saints Heron Quays South Quay Mudchute Island Gardens Shadwell Gunnersbury Richmond Kew Gardens Poplar London Bridge Liverpool Street Sudbury Hill South Harrow North Ealing Park Royal Alperton Northolt Ruislip Gardens Sudbury Town Holborn London City Airport West Silvertown Pontoon Dock Royal Victoria Custom House for ExCeL Prince Regent Royal Albert Beckton Park Cyprus Gallions Reach Beckton Canning Town Hendon Central Crossharbour Fulham Broadway King George V Walthamstow Queen’s Road Langdon Park Chiswick Park Leytonstone High Road South Ealing Osterley Northfields Boston Manor Hounslow East Hounslow Central Hounslow West Heathrow Terminals 1,2,3 Hatton Cross Woodgrange Park Harrow & Wealdstone Hatch End Headstone Lane Carpenders Park Bushey Watford Junction Shepherd’s Bush Market Chalfont & Latimer Chesham Mill Hill East Farringdon Barbican King’s Cross St.

Pancras Woodford Clapham North Shoreditch High Street Covent Garden Earl’s Court Hainault Grange Hill Turnham Green Whitechapel Tower Gateway Rotherhithe Clapham Junction Kensington (Olympia) Acton Central South Acton Surrey Quays New Cross Gate Pinner Heathrow Terminal 4 Oakwood Shepherd’s Bush Heathrow Terminal 5 Woodside Park West Finchley Tufnell Park Archway Highgate East Finchley Totteridge & Whetstone High Barnet Finchley Central Woolwich Arsenal Golders Green Hampstead Brent Cross Colindale Burnt Oak Edgware North Greenwich Imperial Wharf Improvement works may affect your journey, please check before you travel Version A TfL 12.09 Reg.

user No. 09/E/1621/P Correct at time of going to print River Thames River Thames 09/E/1621/P Harringay Green Lanes Northern Metropolitan Victoria District Circle Central Bakerloo DLR London Overground Piccadilly Waterloo & City Jubilee Hammersmith & City National Rail Riverboat services Interchange stations Tramlink Airport Station closed Blackfriars Step-free access from the platform to the street London Overground under construction R OF LONDON Transport for London Bermondsey Southwark Eastcote North Harrow Northwood Hills Northwood Moor Park Queen’s Park Kensal Green Neasden Dollis Hill Willesden Green Kilburn West Hampstead Swiss Cottage St.

John’s Wood Finchley Road Ruislip Manor rth Watford Croxley Harrow- on-the-Hill Preston Road p ners Lane West Harrow Northwick Park Wembley Park Common y Great Portland Street Baker Street Moorgate Aldgate Euston Square Acton Town West Acton East Acton Stamford Brook Ravenscourt Park Hammersmith West Kensington West Brompton Parsons Green Wimbledon Park Southfields East Putney Putney Bridge Wimbledon Victoria South Kensington Gloucester Road Embankment Blackfriars Mansion House Temple Cannon Street Bank Monument Barons Court Fenchurch Street Tower Hill Aldgate East Stepney Green Mile End Bow Road Bow Church Bromley- by-Bow Plaistow Upton Park East Ham Becontree Dagenham Heathway Elm Park Upney Dagenham East Upminster Bridge Hornchurch Upminster High Street Kensington Notting Hill Gate Bayswater Kensal Rise Brondesbury Caledonian Road & Barnsbury Edgware Road Edgware Road St.

James’s Park Sloane Square Westminster Barking Latimer Road Ladbroke Grove Westbourne Park Finchley Road & Frognal Royal Oak Goldhawk Road Wood Lane Lane White City North Acton Kilburn High Road South Hampstead Paddington Chancery Lane Bethnal Green Bond Street Oxford Circus Tottenham Court Road St. Paul’s Marble Arch Queensway Holland Park Lancaster Gate South Tottenham Leyton Midland Road Stratford Wanstead Park Leyton Leytonstone Snaresbrook South Woodford Epping Theydon Bois Debden Loughton Buckhurst Hill Redbridge Chigwell Roding Valley Fairlop Barkingside Newbury Park Wanstead Gants Hill Knightsbridge Hyde Park Corner Green Park Piccadilly Circus Leicester Square Russell Square Caledonian Road Hackney Wick Holloway Road Crouch Hill Arsenal Manor House Turnpike Lane Wood Green Bounds Green Arnos Grove Southgate Cockfosters Waterloo Colliers Wood Morden South Wimbledon Tooting Bec Clapham South Oval Balham Clapham Common Tooting Broadway Stockwell Kennington Borough Old Street Angel Goodge Street Euston Mornington Crescent Camden Town Chalk Farm Regent’s Park Belsize Park Hampstead Heath Canonbury Gospel Oak Hackney Central Dalston Kingsland Homerton Kentish Town West Camden Road Upper Holloway Kentish Town Canada Water Canary Wharf Elverson Road Deptford Bridge Stanmore Canons Park Queensbury Watford High Street Kingsbury South Kenton Kenton North Wembley Wembley Central Stonebridge Park Harlesden Willesden Junction Kilburn Park Maida Vale Warwick Avenue Brondesbury Park Marylebone Lambeth North Elephant & Castle Charing Cross Blackhorse Road Seven Sisters Walthamstow Central Tottenham Hale Finsbury Park Highbury & Islington Pimlico Brixton Wapping New Cross Vauxhall Limehouse Westferry Devons Road Pudding Mill Lane West India Quay Cutty Sark for Maritime Greenwich Greenwich Lewisham Blackwall East India West Ham Warren Street All Saints Heron Quays South Quay Mudchute Island Gardens Shadwell Gunnersbury Richmond Kew Gardens Poplar London Bridge Liverpool Street udbury Hill uth Harrow orth Ealing Park Royal Alperton bury Town Holborn London City Airport West Silvertown Pontoon Dock Royal Victoria Custom House for ExCeL Prince Regent Royal Albert Beckton Park Cyprus Gallions Reach Beckton Canning Town Hendon Central Crossharbour Fulham Broadway King George V Walthamstow Queen’s Road Langdon Park Chiswick Park Leytonstone High Road uth Ealing terley ds w Central Woodgrange Park Harrow & Wealdstone Hatch End Headstone Lane Carpenders Park Bushey Watford Junction Shepherd’s Bush Market Mill Hill East Farringdon Barbican King’s Cross St.

Pancras Woodford Clapham North Shoreditch High Street Covent Garden Earl’s Court Hainault Grange Hill Turnham Green Whitechapel Tower Gateway Rotherhithe Clapham Junction Kensington (Olympia) Acton Central South Acton Surrey Quays New Cross Gate Pinner nal 4 Oakwood Shepherd’s Bush Woodside Park West Finchley Tufnell Park Archway Highgate East Finchley Totteridge & Whetstone High Barnet Finchley Central Woolwich Arsenal Golders Green Hampstead Brent Cross Colindale Burnt Oak Edgware North Greenwich Imperial Wharf Improvement works may affect your journey, please check before you travel Version A TfL 12.09 Correct at time of going to print River Thames 09/E/1621/P Harringay Green Lanes Northern Metropolitan Victoria DLR London Overground Piccadilly Waterloo & City Jubilee National Rail Riverboat services Interchange stations Tramlink Airport Station closed Blackfriars Step-free access from the platform to the street London Overground under construction Transport for London Bermondsey e Aldgate nt Fenchurch Street Tower Hill Aldgate East Stepney Green Mile End Bow Road Bow Church Bromley- by-Bow Plaistow Upton Park East Ham Becontree Dagenham Heathway Elm Park Upney Dagenham East Upminster Bridge Hornchurch Upminster n Barking Bethnal Green South Tottenham Leyton Midland Road Stratford Wanstead Park Leyton Leytonstone Snaresbrook South Woodford Epping Theydon Bois Debden Loughton Buckhurst Hill Redbridge Chigwell Roding Valley Fairlop Barkingside Newbury Park Wanstead Gants Hill Hackney Wick al anor House rnpike Lane Wood Green unds Green Arnos Grove Southgate Cockfosters et Canonbury Hackney Central Dalston Kingsland Homerton y Canada Water Canary Wharf Elverson Road Deptford Bridge Blackhorse Road Seven Sisters Walthamstow Central Tottenham Hale Finsbury Park Highbury & Islington Wapping New Cross Limehouse Westferry Devons Road Pudding Mill Lane West India Quay Cutty Sark for Maritime Greenwich Greenwich Lewisham Blackwall East India West Ham All Saints Heron Quays South Quay Mudchute Island Gardens Shadwell Poplar Bridge Liverpool Street London City Airport West Silvertown Pontoon Dock Royal Victoria Custom House for ExCeL Prince Regent Royal Albert Beckton Park Cyprus Gallions Reach Beckton Canning Town Crossharbour King George V Walthamstow Queen’s Road Langdon Park Leytonstone High Road Woodgrange Park Woodford Shoreditch High Street Hainault Grange Hill Whitechapel Tower Gateway Rotherhithe Surrey Quays w Cross Gate Oakwood Woolwich Arsenal North Greenwich y affect your journey, please check before you travel Olympic Park VeloPark Hockey Centre Eton Manor HandballArena Basketball Arena North Greenwich Arena Lord’s Cricket Ground  St.

John‘s Wood Jubilee Line Hyde Park  Hyde Park Corner Piccadilly Line Horse Guards Parade  Piccadilly Circus Piccadilly Line/Bakerloo Line  Charing Cross Northern Line Bakerloo Line/National Rail Wembley Stadium   Wembley Park Metropolitan Line/Jubilee Line Earls Court   Earl’s Court District Line/Piccadilly Line Greenwich Park   North Greenwich Jubilee Line Royal Artillery Barracks   Woolwich Arsenal DLR/National Rail   Greenwich DLR/National Rail Cutty Sark DLR ExCeL   Prince Regent DLR Custom House DLR Wimbledon   Wimbledon District Line/National Rail Southfields District Line Olympic Stadium   Stratford Central Line Jubilee Line/DLR/National Rail/ London Overground   West Ham Jubilee Line District Line/Hammersmith & City River Thames River Thames 09/E/1621/P Harringay Green Lanes Northern Metropolitan Victoria District Circle Central Bakerloo DLR London Overground Piccadilly Waterloo & City Jubilee Hammersmith & City National Rail Riverboat services Interchange stations Tramlink Airport Station closed Blackfriars Step-free access from the platform to the street London Overground under construction Bermondsey Southwark asden Dollis Hill Willesden Green Kilburn West Hampstead Swiss Cottage St.

John’s Wood Finchley Road Great Portland Street Baker Street Moorgate Aldgate Euston Square Victoria South Kensington Gloucester Road Embankment Blackfriars Mansion House Temple Cannon Street Bank Monument Fenchurch Street Tower Hill Aldgate East Stepney Green Mile End Bow Road Bow Church Bromley- by-Bow Plaistow Upton Park East Ham Becontree Dagenham Heathway Elm Park Upney Dagenham East Upminster Bridge Hornchurch Upminster High Street Kensington Notting Hill Gate Bayswater desbury Caledonian Road & Barnsbury Edgware Road Edgware Road St. James’s Park Sloane Square Westminster Barking Finchley Road & Frognal n ad South Hampstead Chancery Lane Bethnal Green Bond Street Oxford Circus Tottenham Court Road St.

Paul’s Marble Arch Queensway Lancaster Gate South Tottenham Leyton Midland Road Stratford Wanstead Park Leyton Leytonstone Snaresbrook South Woodford Epping Theydon Bois Debden Loughton Buckhurst Hill Redbridge Chigwell Roding Valley Fairlop Barkingside Newbury Park Wanstead Gants Hill Knightsbridge Hyde Park Corner Green Park Piccadilly Circus Leicester Square Russell Square Caledonian Road Hackney Wick Holloway Road Crouch Hill Arsenal Manor House Turnpike Lane Wood Green Bounds Green Arnos Grove Southgate Cockfosters Waterloo Colliers Wood Morden South Wimbledon Tooting Bec Clapham South Oval Balham Clapham Common Tooting Broadway Stockwell Kennington Borough Old Street Angel Goodge Street Euston Mornington Crescent Camden Town Chalk Farm Regent’s Park Belsize Park Hampstead Heath Canonbury Gospel Oak Hackney Central Dalston Kingsland Homerton Kentish Town West Camden Road Upper Holloway Kentish Town Canada Water Canary Wharf Elverson Road Deptford Bridge re Park bury ry y Marylebone Lambeth North Elephant & Castle Charing Cross Blackhorse Road Seven Sisters Walthamstow Central Tottenham Hale Finsbury Park Highbury & Islington Pimlico Brixton Wapping New Cross Vauxhall Limehouse Westferry Devons Road Pudding Mill Lane West India Quay Cutty Sark for Maritime Greenwich Greenwich Lewisham Blackwall East India West Ham Warren Street All Saints Heron Quays South Quay Mudchute Island Gardens Shadwell Poplar London Bridge Liverpool Street Holborn London City Airport West Silvertown Pontoon Dock Royal Victoria Custom House for ExCeL Prince Regent Royal Albert Beckton Park Cyprus Gallions Reach Beckton Canning Town Hendon Central Crossharbour Broadway King George V Walthamstow Queen’s Road Langdon Park Leytonstone High Road Woodgrange Park Mill Hill East Farringdon Barbican King’s Cross St.

Pancras Woodford Clapham North Shoreditch High Street Covent Garden Hainault Grange Hill Whitechapel Tower Gateway Rotherhithe Clapham Junction Surrey Quays New Cross Gate Oakwood Woodside Park West Finchley Tufnell Park Archway Highgate East Finchley Totteridge & Whetstone High Barnet Finchley Central Woolwich Arsenal Golders Green Hampstead Brent Cross Colindale Burnt Oak Edgware North Greenwich perial Wharf Improvement works may affect your journey, please check before you travel Registered user No 09/E/1621/P Olympic Sports Paralympic Sports London 2012 venues The stations indicated are those nearest to the London 2012 venues, which can also be accessed by other stations.

Aquatics Centre

Making the most of the Games In the summer of 2012, the UK will come alive when London hosts the Olympic and Paralympic Games. We aim to create the most accessible and inclusive Games to date, with something to inspire and excite everyone. But you can already join in with London 2012! We want you to use the power of the Games to challenge yourself and push beyond your personal best. Why not try a new sport? Or take part in a cultural activity? How about offering your time and skills as a volunteer? There are endless ways you can be part of this once-in-a-lifetime event. London 2012 is your Games.

What are you waiting for?

Sport Sport is at the heart of the Games but it’s not only for elite athletes. Visit the London 2012 website to find out about the 26 Olympic and 20 Paralympic sports taking place at the Games and use the links to discover how you can get involved. london2012.com/thegames Jobs and skills In addition to the thousands of people needed to build the Olympic Park and stage the Games, there are many opportunities to work on Games-related projects and share a moment of history. We’re recruiting a wide range of people, reflecting the UK’s diversity. london2012.com/jobs Business Businesses throughout the UK are winning contracts for London 2012, with around 75,000 opportunities available.

Visit our Business Network to find out how your organisation, large or small, can benefit. london2012.com/business Education Get Set is our official education programme, designed to involve children and young people in the excitement of the Games. There’s no better opportunity to learn from, and be inspired by, the Olympic and Paralympic Values. london2012.com/getset Volunteering This year we will be launching our Games-time Volunteer Programme. We will be recruiting up to 70,000 amazing volunteers who will help to make sure the Olympic and Paralympic Games run smoothly and successfully. You can find out more and register your interest now.

london2012.com/volunteering Culture There are already hundreds of culture and arts activities underway around the UK bringing the London 2012 spirit to life. Have a look and be inspired to discover talents you never knew you had! london2012.com/culture Inspire The London 2012 Inspire programme officially recognises non-commercial projects and events inspired by the Games. Exceptional schemes across sport, culture, education, sustainability, volunteering and business opportunities can all apply. london2012.com/beinspired Key dates along the road to 2012 2010 2011 2012 During 2010 –  G ames-time Volunteer Programme launched –  I nformation about ticketing available –  C onsultation starts on Torch Relay route – Mascot launched 23-25 July –  O pen Weekend During 2011 – Tickets go on sale – Test Events 27 July – 12 August –  L ondon 2012 Olympic Games 29 August – 9 September –  L ondon 2012 Paralympic Games Join in Ticketing Tickets for the London 2012 Olympic and Paralympic Games go on sale in 2011.

A total of 9.2 million tickets will be available for the Olympic and Paralympic Games.

We aim to give as many people as possible the chance to attend the Games, creating a great atmosphere at all the events. london2012.com/ticketing During 2012 –  L ondon 2012 Olympic and Paralympic Torch Relays