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A Random Walk in the Park

Going straight along the path in the park will take me everywhere before reaching the other gate – a total of 610 meters. However that’s boring and I need more exercise, so instead I’ll try going left or right at random at each crossing till I reach an exit. Now how far do I go on average? This might be a case of too much information! Click here for the answer.

And for a couple of extra points, how far do I go on average if I go left one third of the time and go right two thirds of the time?

path through a park