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 Passing Through (Posted on 2005-04-06)
You are standing in the very corner of a 10 X 10 grid of dots. How many different ways are there to get to the opposite corner of the grid? You must travel through every node once, and only once. You cannot travel diagonally, and you may not go outside of the overall perimeter.

 See The Solution Submitted by Juggler Rating: 3.2500 (4 votes)

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 Solution | Comment 18 of 28 |

I give an example for you to visualise that there are numerous ways to move from one very corner to another end opposite:

1   2   3   4   5   6    7   8   9    10

1   D   L   L   S   R   D   R   D    R    D

2   R   R   R   R   U   R   U   R    U    D

3   D   L   L    D   L   D   L    D     L   D

4   R   D   U   L   U    L   U    L     U    L

5   D   L   R   R    R   R   R    R    R    D

6   R   R   U   D    L   D   L    D    L    D

7   D   L   L    D    U   D   U   D   U     D

8   R   D   U   D    U   D   U    D   U    D

9   D    L   U    L     U   D   U   D   U    D

10  R   R    R    F    U   L   U    L    U    L

Again each letter represent each grid of dot.  S = standing point; R = move to the right from one grid of dot to another. L =move to the left from one grid of dot to the nearer.  U = move upward from one grid of dot to another.  D = move downward from one grid of dot to another; F = finishing point.

The above movement commences from to top corner whereby the letter, S, is indicated.  It begins with the movement to the left 2 steps & after that.....

 Posted by Jonathan Chang on 2005-04-19 15:04:18

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