Using your Head is Permitted

June 2017 riddle

This month's riddle was suggested by Lian Wang. More about its origins will be stated on the solution page.

Consider the following random walk process. The walk is on the real number line. It starts at x0=0. At every step, i, it moves Δi. (So, if it started the step at position xi, it will end up at xi+1=xii.) At each step, Δi is chosen independently and uniformly in the interval [-1,1].

The question: what is the probability, as a function of n, that this random walk visits any negative-valued positions on the number line at any point during its first n steps?

As usual, prove your answer, and please send original solutions only.

List of solvers:

Dan Dima (1 June 18:39)
Lin Jin (4 June 01:59)
Uoti Urpala (4 June 09:54)
JJ Rabeyrin (4 June 18:25)
Ganesh Lakshminarayana (20 June 10:17)

Elegant and original solutions can be submitted to the puzzlemaster at Names of solvers will be posted on this page. Notify if you don't want your name to be mentioned.

The solution will be published at the end of the month.


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