Answer to Question #158077 in Math for Djanel Alva

Question

A mobile game is such that the character will always walk 3 steps North, 4 steps East, 11 steps South and 10 steps West in the same order, over and over again. How far is the character from its original position after doing the procedure 20 times?

Answer 1

After one cycle character is 8 steps to South and 6 steps to West from the starting point. As the straight distance to this point is a hypotenuse of the square triangle with catheti 6 and 8, then its length is $h = (6^2 + 8^2)^{0.5} = 10.$

So, the character will be 10×20 = 200 steps far from its original position after doing the procedure 20 times.