A 10 X 10 X 10 cube is formed of small unit cubes. A grasshopper sits at the center O of one the corner cubes. At a given moment it can jump to the center of any of the cubes which has a common face with the cube where it sits, as long as the jump increases the distance between point O and the current position of the grasshopper. How many ways are there for the grasshopper to reach the unit cube at the opposite corner?
341Surprised this prob is not done yet. Isnt it an extension of the familiar grid problem, where u have to start at one corner and reach the opposite corner with the only allowable moves being to the right and up.
Kaymant sir, here I think it is mean diagonally opposite corner, right?
24just a try..
there are total 27 places to move for grass hopper in XYZ space..
i.e 9 in each X,Y,Z direction
=> first choose 9 out of 27..and then choosing remaining 9 out of 18....the remainig will be fixed automatically
=> no. of ways =(27C9)(18C9)
