Let ABCD be a rectangle with dimensions AB=20 and BC=12 and r be a positive integer.The rectangle is divided into a grid of 20*12 unit squares.The following moves are permitted on the board:one can move from one square to another if the distance between the centers of the two squares is vr.The task is to find a sequence of moves leading with the square with A as a vertex to square with B as a vertex. a.Prove that the task can not be done if r is divisible by 2 or 3 b.Prove that the task is possible when r=73 c.Is the task possible when r=97?

Adhiraj Mandal

13 Years agoGrade 10