# Damn, this must be one very big bowl of pasta...

Algebra Level 4

You are sitting at a table that contains 'n' number of people and 'd' distance away from the person who initially has the bowl of pasta: what is the probability of being the last person to receive pasta?

The Rules are as follows:

1. There is exactly enough pasta for everyone at the table, and every person only takes one serving.

2. The person taking a serving of pasta can only pass it directly to the person left or right (50% chance to go either way)

3. If a person already received pasta and gets the bowl a second time they do not change the direction the bowl is moving in - the bowl keeps going in one direction until it reaches someone who has yet to take a serving (who then has a 50% chance of passing it back).

Write an equation for the probability of being the last person to receive pasta, the equation should hold for all possible values of 'n' from 2 people to infinity, and all values of 'd' (where 'd' it is measured in minimum number of passes from starting person) from d= 1 to infinity.

Because the equation would be hard to plug in - Once you have the equation, count every variable in the equation as = 1 (example, if 'n' showed up twice and 'd' once in the equation count that as 3), every factorial (!) = 10, and every numerical number = 5 (example, if '2' showed up 3 times in the equation count that as 15). Add all of this up, and plug it in!

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