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UPDATE (2 August): The solution this month should be presented
in closed form (e.g. no recursion, no unbounded sums).
We allot a bit-string of length 2n randomly and uniformly from the set of bit-strings containing exactly n zeros and n ones. What is the expected number of prefixes of this string that contain an equal number of zeros and of ones (including the empty string and the full-length string)? As always: prove your answer. |
List of solvers:Jan Fricke (2 August 05:06)Gaoyuan Chen (2 August 15:10) Djinn Lu (2 August 18:21) Albert Stadler (2 August 20:57) Yan Wang (3 August 11:17) Lu Wang (3 August 17:58) Sanlee Xin (5 August 19:04) Joseph DeVincentis (12 August 06:21) Ganesh Lakshminarayana (16 August 02:32) Daniel Bitin (17 August 07:48) Liubing Yu (22 August 11:32) Jens Voss (22 August 17:25) Feifei Ji (24 August 01:13) Wu Zhengkai (28 August 11:05) |
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The solution will be published at the end of the month.
Enjoy!