# Can You Cut The Perfect Pancake?

#### A FiveThirtyEight Riddler puzzle.

By Vamshi Jandhyala in mathematics Riddler

April 23, 2021

## Riddler Classic

Riddler Nation’s neighbor to the west, Enigmerica, is holding an election between two candidates, $A$ and $B$. Assume every person in Enigmerica votes randomly and independently, and that the number of voters is very, very large. Moreover, due to health precautions, $20$ percent of the population decides to vote early by mail.

On election night, the results of the $80$ percent who voted on Election Day are reported out. Over the next several days, the remaining $20$ percent of the votes are then tallied.

What is the probability that the candidate who had fewer votes tallied on election night ultimately wins the race?

## Computational Solution

The probability that the candidate who had fewer votes tallied on election night ultimately wins the race is approximately $\bf{14.82}$.

```
using Distributions
runs = 100000
frac_day = 0.8
frac_mail = 1 - frac_day
num_total = 1000000
num_day, num_mail = trunc(Int32, frac_day*num_total), trunc(Int32, frac_mail*num_total)
succ = 0
for i in 1:runs
votes = rand(Bernoulli(0.5), num_total)
if sum(votes[1:num_day]) < 0.5*num_day && sum(votes) > 0.5*num_total
succ += 1
end
end
print(2*succ/runs)
```