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Mathematical Bases


SparkyDino: Toa of Swordsmanship

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Now if you saw this: LINK, you might've wondered what Bases are. Well, let me explain.

 

Since the beginning of the maths that we know, humans have used Base 10 as a counting system. This may sound complicated, but it is pretty basic. Here's how it works:

 

Every 10 units, you go on to the next set of units. If you count up to ten, what happens after you get to ten? You add a 1 to the start of the number and start counting again. So that's base ten.

 

So why do we use this? Why not base eleven? Why not base six-hundered-and-twenty-six-point-three? Because (here's where it gets simple) We have ten fingers. And ten toes. Convenient, eh?

 

Anyway, for the develepors of maths, it meant that they could count to ten, and then use there toes to keep track of how many tens they had.

 

 

Now, Base Thirteen.

 

It's just like that, but... You count to thirteen before you add a unit. A good example of this is the pounds/stones weight. 14 Pounds until you gain a stone. Not 10 pounds. 14 pounds.

 

 

So what does this mean for the famous 42 theory. Now if you multiply 6 by 9 in base thirteen, an easy way to do it, is to do 6 by 9 in base 10, and then subtract 3 (base 10/base 13) for every 10 you have in there. So if 6 x 9 is 54, that means that you take away 15... which is?

 

41. Oh.

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It's just like that, but... You count to thirteen before you add a unit. A good example of this is the pounds/stones weight. 14 Pounds until you gain a stone. Not 10 pounds. 14 pounds.

And therefore, it's in Base 14. Yes, I have too much time on my hands :P.

 

As for the 42 theory, here's another method that doesn't result in an answer of 41 (or, according to my calculations of 54 - 15, 39 - see what I meant about time?): work out the sum in Base 10, and then divide the result by 13. So, if 6 x 9 = 54 in Base 10, to get the number in Base 13, you divide 54 by 13, giving you 4, with 2 left over. I think you can now see how to get to 42...

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When I said 'it's in Base 14', I meant the example about the stones and pounds, not the 6 x 9 from Hitch-Hiker's Guide to the Galaxy, which IS in Base 13.
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