[Periodicity and Aperiodicity]

Let's start counting the fingers on the right hand: the first is the pinky, the second is the ring finger, the third is the middle finger, the fourth is the index finger, the fifth is the thumb, the sixth is the index finger again, the seventh is the middle finger again, the eighth is the ring finger, the ninth is the pinky, the tenth is the ring finger, and so on. Which finger will be the 2004th in the count?
Notice that from a certain point, a group of eight fingers will start repeating: ring, middle, index, thumb, index, middle, ring, pinky.

## Solution

The first finger is the pinky, and then the group of eight fingers: ring, middle, index, thumb, index, middle, ring, pinky, will keep repeating. When we start listing the fingers, the first one will be the pinky, then the group of eight fingers will repeat 250 times, and then there will be the last three. The third finger in our list is the index finger.

## Answer

Index.

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