Question

How many ways are there to travel in xyz space from the origin (0, 0, 0) to the point (4, 3, 5) by taking steps one unit in the positive x direction, one unit in the positive y direction, or one unit in the positive z direction? (moving in the negative x, y, or z direction is prohibited, so that no backtracking is allowed.)?

Answer 1

I would think you would have to walk the 4 spaces out on the X axis. I would then turn and walk 5 spaces on the Z axis before turning up to walk the last 3 steps on the Y axis.

I think any other way would cause you to move in a negative direction. I hope this helps.