Numbers are wonderful things. We use them to measure things, to calculate, and even to convince people. But sometimes you come across a fact about numbers that just sounds too crazy to be true.

### Every time you shuffle a deck of cards, chances are that you have put them in an order that has never been seen in the history of the universe.

There are 52! (52 factorial) ways to arrange the cards. That’s calculated as 52 x 51 x 50 x 49 x … x 2 x 1 and totals an extremely large number.

Scott Czepiel has come up with a story to explain just how large of a number it is, and to give you an idea, this is how the story begins: Start by setting a timer to count down from 52! seconds. Now, choose a spot on the equator and take one step every billion years. Once you have made it around the earth, remove a single drop from the Pacific Ocean and then walk around the Earth again. Continue doing the same thing over and over until the ocean is empty. Once all of that is done, you won’t even have made a dent in the amount of time left on the timer.

*SEE ALSO: How Many Times Should You Shuffle a Deck of Cards?*

Watch the last 5 minutes of the video below to hear the rest of the story

### In a room of 23 people, there’s a 50 percent chance that two people have the same birthday

In a group of people, there are 23 x 22/2 = 253 pairs of people. The chance of any particular pair having different birthdays is 364/365. However, the chance of all pairs having different birthdays is (364/365)^{253}=0.4995. It may seem counterintuitive, but it’s true. If you increase the number of people in the room to 75, then you are almost guaranteed (with a 99.9 percent chance) that at least two people have the same birthday.

### People tend to associate odd numbers with males and even numbers with females

Research done by James Wilkie and Galen Bodenhausen shows that when people are asked to associate the numbers with genders, they tend to associate odd numbers with males and even numbers with females.

In an article published by the Kellogg School of Management at Northwestern University, the researchers described possible reasons for this: The digit 1 is seen as a “single, stand-alone entity,” whereas 2 “suggests togetherness and cooperation—stereotypically feminine qualities.” Our perception of all numbers could relate to these basic ones.

### There isn’t enough room on the entire planet to write out a googolplex

A googol is 1 followed by 100 zeros. A googolplex is 1 followed by a googol zeros, so basically a really big number. It is so big that that if you were to write the whole thing out in books, they would weigh more than our entire planet — far more in fact. They would weigh about 10^{93} kg, whereas the Earth weighs about 5.972 x 10^{24} kilograms

### There’s no such thing as a boring number in math

We can prove this using what mathematicians call *proof by contradiction*. Let’s say that there were one or more boring numbers (with no special characteristics), let n be the smallest one. Except now n is interesting, because it is the smallest non-interesting number.

### If you look at any particular data set that is long enough, the digit “1” will appear more often than any other

This fact was first observed by physicist Frank Benford in 1983 and doesn’t only apply to 1. In fact, as the size of the digit goes up, the less frequently it is likely to appear.

*SEE ALSO: Are Powerball Drawings and ‘Quick Pick’ Numbers Really Random?*

Think of a set of addresses for example. They start at 1 and go up to a certain number. The digit 9 will only appear as often as the others if the addresses go up to 9, 99, 999, and so on. Benford’s Law is particularly interesting because it is what we call *scale-invariant* — it doesn’t matter what units you measure something in. If your data set is big enough, it will always apply.

According to Ian Stewart in “Professor Stewart’s Cabinet of Mathematical Curiosities,” tax collectors use this fact to detect made-up figures in taxes because people will use each digit equally frequently.

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