39910

If I know the co-ordinates of two points, can I quickly work out how far I will have to walk to get from one to the other?
If the route can be taken without crossing diagonally, (x2-x1) + (y2-y1) = units to reach the opposite point. E.g the points (0,1) and (3,6)
(6-0)+(3-1) = 8 units

How many paths are there from A to B?
= [(x2-x1)+(y2-y1)]! / options east! x options west!
=8!/3!x5! = 56

Alternative methods : drawing a tree diagram via labeling each node as a letter which gives 56 options.
Drawing all the possible routes