40!

41 :D

6x9, base 13

43

-searches up 6x13 base 13-
It's another reference isn't it? How are there so many references!?

On another note, what is a base?

44

A base is basically how many digits you have. Our normal math uses base 10 ("decimal"), because we have ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. You'll hear about binary, which is base 2, because it has two digits: 0 and 1. Base 13 is a number system that has, then, 13 digits; you might choose to label the extra ones A, B, and C.

When you work with a number in a given base (say, base B), then each place value is B times more than the place on its right. In base 10, each digit is worth 10 times more than if it were in the place to its right -- 200 is 10x more than 20, and 30 is 10x more than 3.

So in base 13, you might have the number 2C, which is equal to the number 38 in decimal: 13 * 2 + C (which is 12) = 26 + 12 = 38.

All of the other math you're familiar with works the same way in other bases. You've got to memorize different times tables (3 * 4 = C, for example) and addition wraps around in a different place (9 + 1 = A instead of wrapping around to two digits) but the rules are all the same.

In this case, 6 * 9 can be calculated as adding 9 to itself 6 times, just like in decimal.

9 + 9 = 15 (which is 18 in decimal)
15 + 9 = 21 (which is 27 in decimal)
21 + 9 = 2A (which is 36 in decimal)
2A + 9 = 36 (which is 45 in decimal)
36 + 9 = 42 (which is 54 in decimal)

So, in base 13, 6 * 9 = 42, but 42 is actually 54.

(EDIT: I'm actually not very good with math in base 13; I actually did all of that in decimal and then converted the answers to base 13 afterward. :P Base 2, I'm good with. Base 16, I can add fairly quickly but I can't multiply very well, because it's used a lot in computing.)

45

that's a very good way to explain bases, Coda, thanks!

additionally:

"At the end of the radio series, the television series and the novel The Restaurant at the End of the Universe, Arthur Dent, having escaped the Earth's destruction, potentially has some of the computational matrix in his brain. He attempts to discover The Ultimate Question by extracting it from his brainwave patterns, as abusively suggested by Ford Prefect, when a Scrabble-playing caveman spells out forty two. Arthur pulls random letters from a bag, but only gets the sentence "What do you get if you multiply six by nine?"

"Six by nine. Forty two."
"That's it. That's all there is."
"I always thought something was fundamentally wrong with the universe"

(wiki)

46

The base 13 thing wasn't intended, by the way. Adams said he didn't know about it when he wrote it.

47

that makes sense. it's the math people that figured it out to make sense. =D

Well, the meaning of life, the universe, and this thread... is zero.

*pfft*

and we were having such a nice discussion too. :P

One.

2

Well, if I had said 48, then you would have never posted 49 because that would just have been a loss, and if I HADN'T said 48, then two of you would have come in while I was asleep. So... Didn't have a choice. :P

hmmmmm.... ok, good point there.

Three

Four

Thanks for the explanation Coda! I can understand it now! (It went way over my head when I was searching on the internet = =')

5

Yeah, math pages don't usually cater to laypeople that aren't already into math. Me, I consider it one of my strengths that I can translate intellectual-speak into layman's terms.

Six

Somehow, some websites might give a ton of info and I don't understand it. Then I can go to another website and there's not enough x'D.

20 - 2(7) = 6 base 13
...I think.

Seven

sounds awesome!