yppahpeek

Welcome back travellers! I hope you found the first installment as mind blowing as I did. (I'm not trying to big-up my ego there, I'm not fussed if you enjoyed the way I write, it's the content that completely blows me away!) Just to recap, I am trying to show why it is highly unlikely that any two randomly shuffled decks of 52 cards have ever been the same, even assuming humans could play with cards since the Big Bang! Wow! What a statement! In the last post , I showed how it's possible to count the number of ways of arranging n objects (this is called the number of ' permutations ' of n objects). Without going into too much detail, it works out that for n objects, there are n! permutations (where n! = n x (n-1) x (n-2) x (n-3) x ... x 3 x 2 x 1 ). This means that for a deck of 52 cards, there are 52! , or 8.07 x 10 67 permutations. This is a massive number, and is about equal to a tenth the number of atoms in the whole Milky Way! (This was my own ...

Ever get that feeling, half-an-hour later, when you think "I wish I'd said this "? It takes me a bit longer (about two days). I think what I have learned is that I shouldn't get drunk and start talking about maths. We were having a chilled-out night, having a few drinks and playing some board games. A pack of cards came out. And I drop the bomb: Did you know? "It is very unlikely that any two randomly shuffled decks [of 52 cards] will ever have had the same order in the history of the world – even if the world's population had started playing cards at the Big Bang" – Alex Bellos. Alex's Adventures in Numberland. pg339. I don't think the significance of this properly hit. Or maybe it did and I just couldn't answer the questions. "No, really? No way!" "Since the beginning of the universe?". I mumbled something about a number being followed by 67 zeroes, but I don't think the true awesomeness of this really hit. To...

If you're kind of into maths, then Alex's Adventures in Numberland will totally blow you away. Even if you're not that interested by maths, the book is so packed full of exciting and fascinating 'dispatches from the world of mathematics' that you will find yourself testing some of the ideas. The book has linked me to some pretty amazing web pages that have found innovative ways of displaying a series of numbers. The first I want to link to is the On-Line Encyclopedia of Integer Sequences . Way back in the pre-internet days of 1963, mathematician Neil Sloane started to collect sequences of numbers. Writing on pieces of card, he would diligently give reference numbers to all of his series. For example, the sequence of natural numbers (1,2,3,4,5,6,7,8,9,10...) was given the label 'A27'. By the mid-nineties, the list contained over 5,000 distinct number sequences. Of course, then 'the internet happened', and Sloane now receives roughly 10,000 submis...