# Five things you didn’t know about… Mathematics

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Being an enthusiastic mathematician, I feel compelled to share some of the most weird and wonderful (and let’s face it; often useless) facts in the world of maths.

Numbers - By Ianmacm via Wikipedia Commons

1. Size doesn’t matter - Think of the biggest finite (non-infinite) number you can think of. Got one? Well how about 10100, commonly referred to as a googol, a number consisting of 1 followed by 100 zeroes. Now how about 10googol; a “Googolplex” is a number consisting of 1 followed by a googol zeroes. This number is so large that if you tried to write it out (assuming you never grew old or tired, and your pen would never run out) there is not enough physical space in the known Universe to even come close to finishing. This remains true even if you could write so small that a zero took up as much space as a single proton.

2. Stay happy! -You’ve no doubt heard of different types of numbers: Integers, prime numbers, rational numbers, etc. But did you know there’s a set of numbers known as “Happy Numbers”? Take a number, square each of its digits, add these up, and keep going until you hit a 1 (a happy number) or a never ending loop (a sad number). Who said maths is too serious?

3. Happy birthday to you, and you… and you…? – Some probability now, exciting I know. Let’s say you have a room of 23 people, what would you say is the probability of any two people sharing a birthday (365 possibilities per person)? Would you expect it to be pretty low? In fact, it’s slightly over 50%. And to reach a probability of 99%, one only needs a room containing 57 people. This seems odd, but it’s true. The process involves the use of factorials and binomial coefficients, so I’ll spare you the proof.

4. You don’t get something for nothing – Take a look at the animation below; you are given a triangle, and simply by moving around a few its pieces, we end up with a triangle that seems to contain a brand new square. This is called the missing square puzzle, and actually has quite a simple solution; it requires little to no mathematical knowledge, so see if you can work it out.

Missing Square Puzzle – By Trekky0623 via Wikipedia

5. I’m sure it’s around here somewhere…– This last one is kind of a riddle, but it shows the confusion in simple distribution of numbers;

“Three guests are charged £10 each for their rooms. The manager receives the £30, but decides to issue a cost of only £25, giving the further £5 to the porter to return to the guests. Because of difficulty in dividing, the porter decides to give £1 each back to the guests, and thus keep the remaining £2.

Since each guest has retrieved £1, their total payment is £9 each and £27 in total. The porter has kept £2 for himself. This makes a total of £29, but the guests originally handed over £30, where’s the missing £1?”