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Mar 25, 2025

Any time you shuffle a deck of cards (7 "riffle shuffles" to be a truly random shuffle), you have almost certainly made a shuffle that no one has ever made before. There are approximately 8 × 10^67 (80,658 vigintillion) possible orders of a deck of cards, more than the number of atoms in the universe.

This is because when ordering the deck you have 52 choices for your first card, then 51 for your second card, and so on until you have 1 choice left for your 52nd card. This means that you have 52 factorial (denoted 52!) possible orders of a deck of cards.

52! = 52 × 51 × 50 × ... × 3 × 2 × 1

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Mar 4, 2025

Why do we sometimes get sunken dark areas under our eyes when we don't sleep well?

A lack of sleep makes the delicate under-eye area more susceptible to changes in blood flow, fluid balance, and skin tone, resulting in the characteristic dark circles and sunken appearance.

Inadequate sleep throws off the delicate balance of hormones and the nervous system that regulate circulation. This can lead to increased stress hormones, increased inflammation, and fluid imbalances.

When you don't get enough rest, your body releases stress hormones that can cause blood vessels under the thin eye skin to dilate, making them more visible and appearing darker. Additionally, inadequate sleep can hinder normal circulation, leading to blood pooling in these vessels, which also contributes to the darkened appearance.

Furthermore, lack of sleep can cause fluid retention, leading to puffiness under the eyes. This puffiness can cast shadows, further enhancing the look of dark circles. The skin in this area is already delicate and thin, and poor sleep can make it appear even more translucent due to the reduced blood circulation, allowing the underlying blood vessels and any discoloration to be more noticeable.

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Feb 11, 2025

The jackfruit is the world's largest tree fruit, reaching as much as 120 pounds (55 kg) in weight. Jackfruit trees are native to tropical areas of the Indian subcontinent and Southeast Asia.

A man next to a tree filled with jackfruits.
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Feb 10, 2025

Polaris (the North Star) is around 430 light-years away from Earth.

A light-year is the distance that light travels in one year. Light travels approximately 299,792,458 meters per second in the vacuum of space. This means a light-year is approximately 9,461,000,000,000 kilometers.

Because of the time that light takes to reach us from such an unfathomably far away distance, when we see light from the North Star we are looking into the past. The light we see when we look at the North Star has just arrived after journeying towards us for the past 430 years. So we are seeing the North Star as it was centuries ago.