Friday, 20 December 2013

Check out our Xmas card - 1 seasonal message with 1,024 different image combinations that will not repeat in sequence for another 12,252,240 seconds.

Because it wouldn't be Christmas without some pointless trivia...

There are 16 fixed windows and each window contains two images, which is a total of 32 images. This means that there are 1,024 possible combinations: (16 x 2) x (16 x 2) = 1,024.* However, if the 32 images loaded randomly in the 16 windows, the potential combinations are huge. In order to find out how huge, it is necessary to calculate ‘the factorial n!’ (32! =). This number is arrived at by calculating 32 x 31 x 30 x 29... and so on, all the way down to 1.  If we had arranged for the 32 images to load randomly, the potential combinations would be more like this:


Put another way, that's 263 decillion 130 nonillion 836 octillion 933 septillion 693 sextillion 530 quintillion 167 quadrillion 218 trillion 12 billion 160 million.* That's a brain-achingly big number, especially if you consider the universe has only been around for approximately 432,329,886,000,000,000 (432 quadrillion 329 trillion 886 billion) seconds.*

Each box window rotates at a different frequency - 2 seconds (top left) through to 17 seconds (bottom right) increasing in one second intervals. When the boxes start opening, so begins a sequence that will not catch up with itself for another 12,252,240 seconds.  The reason it takes so long is because of the ‘lowest common multiple’. The  ‘lowest common multiple’ is the first number that two different numbers share when multiplied. For example, the lowest common multiple of 6 and 7 is 42 (which all Hitchhiker's Guide to the Galaxy fans know to be the answer to the ultimate question).  The ‘lowest common multiple’ of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ,13, 14, 15, 16 & 17 is: 12,252,240*

So how long exactly is 12,252,240 seconds?
12,252,240 = 204204.0 minutes or 3403.4 hours or 141.8 days (or some time in May 2014 if you’re reading this in December 2013)

However, if you haven’t got one hundred and forty one point eight days to wait to see the sequence  repeat - there is an easier way -  click “home” or refresh the landing page to see the message sequence start again.

*If you feel any of the numbers or calculations above are not correct, please let us know, but do remember, it's just a bit of fun!

Once again - we hope you have a Merry Christmas and a Happy New Year.

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