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More than 19,000 light-years. A mole numerically is about 6.022 x 10^23, which is 600 billion trillion. Even a miniscule height means an astronomically tall stack.

Using a figure of 5/8 inch (1.6 cm) for a deck of 54 cards, you get a card thickness of about 0.0003 meters per card. Multiplying, we find that a "mole" of cards creates a stack about 1.8 x 10^20 meters, or 1.8 x 10^17 kilometers. A light-year is only 9.46 x 10^12 kilometers. Dividing, we get a figure of about 1.9 x 10^4 or 19,000 light years.

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