Cents per cents

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This is my version of a puzzle I originally saw on Alex Bellos's Puzzle Block.

Puzzle

100 of the dimmest bank robbers recently broke in to the Denver Mint and made off with a truck-load of fresh new pennies. To divvy up their loot, they decide that the youngest thief will get 1% of the score, then the 2nd youngest will get 2% of what is left, the third youngest getting 3% of what is left after that, and so on, until the oldest (100th youngest) gets 100% of what is left after everyone has taken their share.

Which thief receives the largest share? Further, what is the least amount of money he will leave with, assuming no rounding occurs while splitting the take?

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