Science Explorer recently ran a feature looking at a series of mathematic quirks, and a selection of these are examined here. Maths and numbers often produce unusual patterns and challenges.

*Birthday surprise*

How likely is it that two people share the same birthday? This, naturally, depends on the odds which relates to the number of people within a given area at a given point in time.

For example, if you are 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.

To explain this, if you increase the number of people in the room to 75, then it is near certain (with a 99.9 percent chance) that at least two people have the same birthday.

*Card shuffling*

When a deck of cards is shuffled, there is a chance the order produced is one not seen before in the history of the universe. This comes down to factorials.

With this, there are 52! (52 factorial) ways to arrange the cards. This is calculated from 52 x 51 x 50 x 49 x 48 x 47 and so on….which ends up with a very large number.

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.

*How big is a googolplex?*

A googolplex is a very big number. A googolplex is the number 10^{googol}, or equivalently, 10^{(10100)}, designed to represent one, followed by writing zeroes until you get tired! It is estimate the total number of elementary particles in the universe is around 10^{80} (what’s known as the Eddington number).

There isn’t enough room on the entire planet to write out a googolplex. The number is so big that to copy put into books would mean the books would weigh more than our entire planet.

*The most common digit is ‘1’*

In any given set of data, the digit “1” will appear more often than any other. In fact, as the size of the digit goes up, the less frequently it is likely to appear. Think of it as a street of houses; most roads begin with house number ‘1’ and then steadily increase, but ‘1’ will occur most often.

These are just a few of the maths and number puzzles designed to challenge humankind.