A mathematician has an enormous cake and many friends with whom to share it.

###### This problem is part of the Advent Calendar 2015.

First, she gives a quarter of the cake to the first friend.

She then gives a fifth of the remaining cake to the next friend. She then gives a sixth of the now remaining cake to the next friend. This process continues until she gives a hundredth of the remaining cake to the last friend.

She finally takes the portion that is left over for herself.

What percentage of the original cake does she have?

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