$($a$)(5$ points$)$

Toe's Pizzeria is hosting a special event where they're generously offering a unique pizza

adorned with a layer of supposedly edible gold dust to one fortunate $($or perhaps not$-$so$-$

fortunate$)$ NYU student. You find yourself as the recipient of this extraordinary pizza and

decide to share the culinary joy in Washington Square Park. The pizza, $n$ units large, prompts

you to extend the your generosity to your friend group, consisting of $8$ individuals, yourself

included.

Embarking on a sharing spree, you slice the pizza into $8$ equal portions, devouring one while

distributing the rest. Remarkably, $4$ of your friends belongs to other disjoint friend groups of

Extending the generosity, these $4$ friends repeat the slicing ritual. Amazingly, every friend

group has $4$ members who continue the ritual. This communal pizza enjoyment continues

until the cut slice reaches a minimal size of $1$ unit. Formulate a recurrence relation in terms

of the total number of slices and solve using any method.

Solution: INSERT YOUR SOLUTION HERE