MathDB
The most complex coin ever (BMT 2019 Algebra #8)

Source:

May 6, 2019

Problem Statement

A biased coin has a 6+2312 \dfrac{6 + 2\sqrt{3}}{12} chance of landing heads, and a 6−2312 \dfrac{6 - 2\sqrt{3}}{12} chance of landing tails. What is the probability that the number of times the coin lands heads after being flipped 100 times is a multiple of 4? The answer can be expressed as 14+1+abc⋅de \dfrac{1}{4} + \dfrac{1 + a^b}{c \cdot d^e} where a,b,c,d,e a, b, c, d, e are positive integers. Find the minimal possible value of a+b+c+d+e a + b + c + d + e .
Back to ProblemsView on AoPS