Day 25: Spread The Christmas Spirit!

Algebra Level 1

To end this Advent Calendar, let's finish by wishing everyone a Merry Christmas!

At the beginning of Christmas only one person (Santa) has the Christmas Spirit.

At the end of every hour every person with the Christmas Spirit infuses \(3\) new people with the Christmas Spirit, unless everyone already has the Christmas Spirit. (There is no overlapping; only one person can infuse a specific person.)

Assuming that the world has approximately \(7\ \mathrm{billion}\) people, will everyone in the world be infused with the Christmas Spirit by the end of the \(24\) hours of Christmas Day?

(Yes, forget about time zone difference as Christmas Day is obviously relative to Santa time :) )

(If you are being very pedantic, you can assume that the people take it in turns to infuse others at the end of each hour)

This problem is part of the Advent Calendar 2015.

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