Batch 2 - Class 67 - The Orange Game (Routing and Deadlocks)

• Infinite Circles of Resistors  - In the circuit below colored lines are 1 Ohm resistors, and black lines are connecting wires. The first (innermost) circle has 8 resistors, the next 16, the next 32 and so on infinitely. What is the total resistance of the circuit?

• Answer: 1/4 Ohm

• Traffic Jams - why do they happen? Illustrate.

  Think of them as everyone trying to use the "crossing" at once. What needs to be done when a jam happens? Some people get out of their cars and try to clear the jamOften it requires people to cooperate rather than be greedyWhen you have a lot of people using one resource (such as cars using roads, or messages getting through the Internet), there is the possibility of “deadlock”. A way of working cooperatively is needed to avoid this happening. 
• Lets play the Game

  Groups of 5 or more in a circleEach kid has a color that they must get. There are two balls of each color (except one color which has one ball). Initially, all balls are at incorrect places. A neighbor may pass a ball to a someone who has empty hand. The kids must work to get everyone their respective colorsCount the number of steps in solving itWhat strategies did kids follow to solve the problemGreedy or not?What new rules can make the problem easier to solve?What does it mean in terms of a network?Does this impose a higher cost?Different configurations (Count number of steps)What if you had 4 people at corners of square and one in center (one in center has all other four as "neighbors")?What if all were in a straight line?What if the game has to be done without talking on each tick of clockNotion of "lock"Real examples of "locking" - what if two people were trying to update your bank account at same timeRead, add/subtract, Write operationsDeadlocks with locking (taking money from one account and putting it in another)

• What would happen to the earth if the entire population of earth gathered in one place, say Delhi, and then jumped at once?

  Delhi is 1484 sq km, so if we can fit 5 people per square meter, then we can get 7 billion people in DelhiWhat is current population of Delhi? About 17 MLets say everyone jumped by a meter. What will happen to earth?Earth will move back by collective mass*distanceSay, every person is 45 kg, so total about 300 billion kgHow heavy is earth? 6 x 10^24 kgSo, how much would the earth move? About 10^(-14) meters, so a fraction of a nanometerHmm, not much happened, everyone will wonder why they came to Delhi and jumped!Now what happens - let kids run amok with cell phones, people trying to get out of Delhi, food/water, etc etcMobile phonesWith Delhi's population, perhaps there is capacity for less than 1M calls every 10 minutes?Over 1000 hours for every person to get a chance if they all coordinated well and no one tried to make multiple callsTransport outDelhi train station handles 500,000 passengers dailyAirport 100,000 passengers dailyRoads - 6 major exits, say 4 cars (20 people) per 5 seconds, so 200,000 passengers can leave daily Lets say, total 1M people can leave dailyThat would be 7000 days (20 years) for them to get outFood and Water availabilityWith so many people, there would be no space to store food!

• (Geoffrey - 150) Five boys and five girls found five pennies. It was decided to arrange the group in circle, and count out individuals at fixed intervals, giving them a penny as they leave. A clever boy came up with a scheme to arrange the kids in the circle so that all the boys would count out first. The girl standing at the first place, though, insisted that she be allowed to determine the interval, and arranged it so that all girls got counted out first. The arrangement in the circle was as under (Start at 1, and go clockwise). What were the intervals the boy and the girl thought of?

• Answer: Boys 14, Girls 13