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        riddles >> medium >> Ant on a grid
        
(Message started by: Altamira_64 on Feb 4^th, 2013, 4:54am)

Title: Ant on a grid
Post by Altamira_64 on Feb 4^th, 2013, 4:54am

An ant is walking on a grid like in the attached shape and wants to go from A to B. How many different routes can it follow, but with exactly the same distance?

Title: Re: Ant on a grid
Post by rmsgrey on Feb 4^th, 2013, 5:12am

Assuming: [hide]it follows the lines and requires the shortest distance[/hide]
There are: [hide]56 ways[/hide]

Changing the assumptions may change the answer

Title: Re: Ant on a grid
Post by Altamira_64 on Feb 4^th, 2013, 7:23am

Indeed it follow the lines and the distance should always be the same, i.e. 8a, where a is the side of the rectangle (yes, they are rectangles, although it is not clearly shown on the shape!).

Title: Re: Ant on a grid
Post by Grimbal on Feb 4^th, 2013, 9:29am

Actually, it doesn't matter what the proportion is. Or even whether the spacing is uneven. The result remains the same.

Title: Re: Ant on a grid
Post by rmsgrey on Feb 5^th, 2013, 4:36am

on 02/04/13 at 09:29:40, Grimbal wrote:

Actually, it doesn't matter what the proportion is. Or even whether the spacing is uneven. The result remains the same.

It's sufficient, though not necessary that the lines that look parallel are both straight and parallel.