Program Output for May 2016 Puzzler:
1) Doing a random walk through the puzzle for 100000
trips. This takes a while, please be patient.
Found: 982 valid paths.
2) Make a list of possible paths ignoring center obstruction
and test each for validity.
Found: 982 valid paths.
The above two sets are equal? True
3) Using combinations:
Number of paths A to Point(3,4) and
(from Point(3,4) to B): 35
Number of paths A to Point(4,3) and
(from Point(4,3) to B): 35
Number of total paths A to B without center the obstruction: 3432
Number of valid puzzle paths is equal to the total number of
paths without the obstructions minus the number of paths
that pass through Points(3,4) and (4,3). The paths through
Point(3,4) is the number of paths from A to Point(3,4) times
the number of paths from Point(3,4) to B (ditto for Point(4,3)).
Number of valid paths = 3432 - 2 * (35 * 35) = 982