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.
The following is one of the example:
1 2 3 4 5 6 7 8 9 10
1 R R R R R R R R R D
2 U D L L L L L L L L
3 U R R R R R R R R D
4 U D L L L L L L L L
5 U R R R R R R R R D
6 U D L L L L L L L L
7 S D R R R R R R R F
8 D R U L L L L L L L
9 D R D R D R D R D U
10 R U R U R U R U R U
Each letter represents the movement from one grid of dot to another adjacent grid of dot.
S = the standing point
F = Finishing point
U = Move from one grid of dot upward to another nearby grid of dot
D = Move from one grid of dot downward to another nearby grid of dot
L = Move from one grid of dot to the left nearby grid of dot.
R = Move from one grid of dot to the right nearby grid of dot.
The movement begins from the 'S' and moves upward. After that, follows the letter that is indicated to move left or right or up or down.
The above example shows that it is possible to move from one grid of dot to the opposite.
The question does not mention the starting point must be in the very left hand corner & that the finishing point must be in the very right hand corner. Thus, it can begin any point in the middle of the grid of dot but it must be ended in opposite side.
The above is just one of the way to solve it.
Nevertheless, there are numerous possible ways to solve the question.
Edited on April 19, 2005, 1:06 am
Solution
