Day 25: Spread The Christmas Spirit!
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 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 people, will everyone in the world be infused with the Christmas Spirit by the end of the 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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1 solution
Every hour the number of people with the Christmas Spirit quadruples, as given by the conditions in the question. So the maximum number of people able to be infused with the Christmas Spirit by the end of Christmas Day is 4 2 4 .
Now note that 4 5 = 1 0 2 4 > 1 0 0 0 , so 4 2 0 = ( 4 5 ) 4 > 1 0 0 0 4 > 7 , 0 0 0 , 0 0 0 , 0 0 0 by a long way.
Since 4 2 4 > 4 2 0 , we have that 4 2 4 > 7 b i l l i o n and so y e s , everyone will be infused with the Christmas Spirit by the end of the day!