There are 100 towns in a country. Each of them is connected with every other town by a one-way road. It is possible to change the direction of traffic on one of the roads such that after this operation each town can still be reached from any other.⚡aYesbNocMay beSubmit

There are 101 towns in a country. Some pairs of towns are connected by one-way roads, and there are exactly 40 roads going into and 40 roads leaving each town. Can you reach each town from any other, driving along at most three roads?⚡aYesbNocMay beSubmit

There are 30 towns in a country. Each of them is connected to every other by a single road. What is the maximum number of roads that can be closed in such a way that one can still reach each town from any other?

The government of a certain developing nation wants to improve transportation in one of its most inaccessible areas, in an attempt to attract investment. The region consists of several important locations that must have access to an airport.Of course, one option is to build an airport in each of these places, but it may turn out to be cheaper to build fewer airports and have roads link them to all of the other locations. Since these are long distance roads connecting major locations in the country (e.g. cities, large villages, industrial areas), all roads are two-way. Also, there may be more than one direct road possible between two areas. This is because there may be several ways to link two areas (e.g. one road tunnels through a mountain while the other goes around it etc.) with possibly differing costs.A location is considered to have access to an airport either if it contains an airport or if it is possible to travel by road to another location from there that has an airport.You are given the cost of building an airport and a list of possible roads between pairs of locations and their corresponding costs. The government now needs your help to decide on the cheapest way of ensuring that every location has access to an airport. The aim is to make airport access as easy as possible, so if there are several ways of getting the minimal cost, choose the one that has the most airports.

Globally, there is a pattern of movement away from cities to regional and rural areas.Group of answer choicesTrue

Consider all scenarios in which we have a city on a flat plane in which all roads are straight lines; the points at which two (or more) roads meet are called junctions; and we have two points A and B that are accessible from each other by road.In this question you have to determine whether the following statement is true or false.Among all possible routes between A and B, the shortest route goes through the fewest number of junctions.The following points may be helpful:Consider using a pen and paper to draw a few maps when thinking about this problem.The statement is about all possible scenarios, not just a particular city map that you may happen to draw. The statement is about all maps imaginable (with the above-mentioned properties). Obviously you cannot draw all possible maps, so you need to reason about this problem.The statement is true if you can convince yourself that it holds in all possible maps for all possible pairs of locations A and B. The statement is false if you can draw a map in which the statement does not hold.You can assume all distances are finite.Is the statement true or false?