find the number of paths that you could take to travel from A and B if you are only allowed to move to the right or down through the grid. You cannot travel a path if the path is not drawn in .

Determine the number of pathways that we can take to go from point A to point B, if we can only travel along the intersected points and can only go South or East.

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?

From A, Radhika travels 8 km towards north. Then she takes a turn and travels 8 km towards east. Again, she turns right and travels 16 km to reach B. In which direction must Radhika travel from B to reach A, so that the distance would be minimum?

My First Geometry ProblemYou are on a 22-dimensional grid, where you start at (0,0)(0,0).You are given a binary string 𝑆S of length 44 where:𝑆1S 1​ refers to left direction;𝑆2S 2​ refers to right direction;𝑆3S 3​ refers to up direction;𝑆4S 4​ refers to down direction.𝑆𝑖=1S i​ =1 denotes that you are allowed to make a move in the respective direction and vice-versa.Find the number of cells (𝑥,𝑦)(x,y) you can possibly visit which satisfy −10≤𝑥,𝑦≤10−10≤x,y≤10.Note that:You always include the cell (0,0)(0,0) in your answer.If you can visit (𝐴1,𝐵1)(A 1​ ,B 1​ ) and (𝐴2,𝐵2)(A 2​ ,B 2​ ) individually, but not both at the same time, you will still include both of them in your answer.Moves are defined as:A move in left direction is a move from cell (𝐴,𝐵)(A,B) to (𝐴−1,𝐵)(A−1,B).A move in right direction is a move from cell (𝐴,𝐵)(A,B) to (𝐴+1,𝐵)(A+1,B).A move in up direction is a move from cell (𝐴,𝐵)(A,B) to (𝐴,𝐵+1)(A,B+1).A move in down direction is a move from cell (𝐴,𝐵)(A,B) to (𝐴,𝐵−1)(A,B−1).Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of a binary string 𝑆S of length 44 - denoting the directions in which moves are allowed.Output FormatFor each test case, output on a new line, the number of cells you can visit as mentioned in statement.Constraints1≤𝑇≤151≤T≤15∣𝑆∣=4∣S∣=4𝑆𝑖∈{0,1}S i​ ∈{0,1}𝑆𝑖=1S i​ =1 for at least one 1≤𝑖≤41≤i≤4.Sample 1:InputOutput5001011000110111011111121121231441Explanation:Test case 11: The only allowed direction is up. Thus, you can only visit cells (0,0),(0,1),(0,2),…,(0,10)(0,0),(0,1),(0,2),…,(0,10); which are a total of 1111 cells.Test case 22: The allowed directions are left and right. Thus, you can visit cells (−10,0),(−9,0),…,(0,0),…,(9,0),(10,0)(−10,0),(−9,0),…,(0,0),…,(9,0),(10,0), which are a total of 2121 cells.Test case 33: The allowed directions are right and up. You can visit all cells (𝑥,𝑦)(x,y) such that 𝑥≥0x≥0 and 𝑦≥0y≥0, which are a total of 121121 cells.Accepted195Submissions293

A boy lives at X and wants to go to School at Z. From his home X he has to first reach Y and then Y to Z. He may go X to Y by either 7 bus routes or 8 train routes. From there, he can either choose 5 bus routes or 6 train routes to reach Z. How many ways are there to go from X to Z?