**Problem of the Week**

**Math Club**

**BUGCAT 2020**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

**BingAWM**

pow:problem3f20

Problem 3 (due Monday, October 12)

An outcome of flipping a coin $n$ times is called $k$-lucky if it contains a pattern which is repeated
$k$ times in a row. For example, the outcome THHTHTHTTH (T stands for “tales” and H
for “heads”) of flipping a coin 10 times is 3-lucky since HT appears 3 times in a row. Let $P_n$ be the probability that flipping a coin $n$ times is $6$-lucky. Find $t$ as small as you can so that $P_n<t$ for all $n$.

Only one solution was received, form Yuqiao Huang. His solution and some additional comments are contained in the following link Solution

pow/problem3f20.txt · Last modified: 2020/10/22 16:05 by mazur

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Noncommercial-Share Alike 3.0 Unported