## The ideal number.

For the discussion of math. Duh.

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neoliminal
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### The ideal number.

Someone was saying that 10 was the ideal number in the main comic thread (bemoaning the number of planets being 8). Noted was that 9 has a square root of 3, while 12 is very pleasing in different base systems.

So what is your ideal number and why?
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Tirian
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### Re: The ideal number.

Ideal for what?

Not waiting for the answer, I'll go ahead and say that six is an under-appreciated number. It's easy to multiply numbers in base-six, and it's easy to count off on one hand. (I've never quite understood why people think that your base has to be based on the number of fingers that you have instead of one more.) In addition, it's within ordinary human mental capacity to remember and differentiate between six things, so its natural to have six main characters in a television show or breaking a problem into six pieces.

jroelofs
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### Re: The ideal number.

Six is also cool because: 1+2+3 = 6 = 1*2*3.

doogly
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### Re: The ideal number.

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Talith
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### Re: The ideal number.

I've always been partial to 64. I think it stems from my noting that it was a square and a cube before the fact was brought up in class. It's the same reason that I like multiplying numbers by 9, because I found a pretty quick method before it was taught to us.

t0rajir0u
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### Re: The ideal number.

Dason
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### Re: The ideal number.

42. Need I say more?
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Shivari
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### Re: The ideal number.

Talith wrote:I've always been partial to 64.

ME TOO! =D

(No idea why, though)

It's the same reason that I like multiplying numbers by 9, because I found a pretty quick method before it was taught to us.

Is it the 9 times x is just whatever the higher 10 is minus x? (e.g. 9 x 6 = 54 = 60 - 6) That trick made multiplying by 9 way more intuitive in 5th grade.

Charlie!
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### Re: The ideal number.

42.
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Quigibo
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### Re: The ideal number.

3711251

Its ideal if you convert it to base 26 with alphanumerics (with 'a' being zero)
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Flightless_bird
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### Re: The ideal number.

I like 27. Mostly because I like 3 and 27 is 3^3
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thicknavyrain
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### Re: The ideal number.

ThickNavyRain in the "Number war" thread wrote:I chose 6!
Many of the measurements of time are in multiples of 6 (60 seconds, 60 min, 24 hours)
6 is also a perfect number (multiples = 1, 2, 3. 1+2+3=6)
Only number that is both the sum and the product of three consecutive whole numbers (1,2,3)
It's a highly composite number
It's a triangular number as is it's square (36).
6 Rules. (12 does to, but you can consider it what 20 is to 10 in base 6).
I love 6.
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minno
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### Re: The ideal number.

I like 2520, since all numbers up to 10 are its factors. A lot of my first programming experience was making programs to compute factors of numbers.
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gorcee
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### Re: The ideal number.

64 is my lucky number, for a variety of reasons.

TheWaterBear
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### Re: The ideal number.

t0rajir0u wrote:24.

I thought I was the only one! 24 ftw!

Turtlewing
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### Re: The ideal number.

I'm fond of 26, mostly because it has some history in an PRG group i was in during high school (White Star 26 was a recuring ship, even in settings not associated with Babylon 5). I think it was also the name of the little dinosaur in the Dinotopia miniseries.

As for bases, i like base 8, because it converts intuitively to binary and doesn't require more digets than you're used to (unkile hexidecimal).

Macbi
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### Re: The ideal number.

At the moment I think 71 and 77 are pretty cool, because they don't look interesting but have connections to the Look-and-Say sequence and Egyptian primes respectively.
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mr-mitch
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### Re: The ideal number.

6 is also cool because the volume and surface area of a cube with sides of length 6 units are both 216 units(squared or cubed).

PM 2Ring
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### Re: The ideal number.

Talith wrote:I've always been partial to 64. I think it stems from my noting that it was a square and a cube before the fact was brought up in class. It's the same reason that I like multiplying numbers by 9, because I found a pretty quick method before it was taught to us.

Me, too. But then I learned about the index laws & factorization, and realize that this nice property of 64 was just another manifestation of the awesomeness of 6.

And here's some more 6 awesomeness:

Golomb ruler of order 4 and length 6. This ruler is both optimal and perfect.

Kurushimi
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### Re: The ideal number.

I think I need to make some remarks about 3.

Have you heard about the scale riddle? You have 8 balls, and all of them weigh the same except one, which is heavier than all the rest. Your job is to find the heavy ball with the least amount of weighings. Many people assume you need 3 weighings to do this, but you can do it in 2. In fact, with n balls, instead of log_2 n tries, it takes log_3 n tries to do it.

Also, every number can be represented as the sum and difference of unique powers of 3.

1 = 1
2 = 3 - 1
3 = 3
4 = 3+ 1
5 = 9 - 3 - 1
6 = 9 - 3
7 = 9 - 3 + 1

And so on. I'm also pretty sure 3 is the only number with that property.

Certhas
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### Re: The ideal number.

4 = 2+2 = 2*2 = 2^2
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Xanthir
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### Re: The ideal number.

Certhas wrote:4 = 2+2 = 2*2 = 2^2

It also equal 2^^2, 2^(3)2, and all higher tetrations.
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PM 2Ring
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### Re: The ideal number.

For every property of the natural numbers, there must be a smallest number with that property. And since there are a lot more interesting properties than there are small numbers, plenty of small numbers turn out to be interesting for multiple reasons, 2 being a fairly notorious example.

http://en.wikipedia.org/wiki/Strong_Law_of_Small_Numbers wrote:"The Strong Law of Small Numbers" is a humorous paper by mathematician Richard K. Guy and also the so-called law that it proclaims: "There aren't enough small numbers to meet the many demands made of them."[1] In other words, any given small number appears in far more contexts than may seem reasonable, leading to many apparently surprising coincidences in mathematics, simply because small numbers appear so often and yet are so few.

Another nice property of 10:
(1²+1) (2²+1) = (3²+1) = 10

Yakk
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### Re: The ideal number.

My favourite prime is 91.
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Tirian
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### Re: The ideal number.

Yakk wrote:My favourite prime is 91.

It's certainly pretty cool that it the largest prime that is divisible by 7.

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### Re: The ideal number.

I think Yakk's point is that it is, iirc, the only number under 100 which passes the easy tests for compositeness - divisibility by 2, 3, and 5 (which are the easiest divisibility tests in base 10), divisibility by 11 (which is easy for numbers under 100), and being a perfect square - and yet fails to be prime.
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ceaser13
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### Re: The ideal number.

Call it the romantic in me.
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Osha
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### Re: The ideal number.

Take a disk image of Boom Blox Bash Party
Convert it to a (very long) integer.

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### Re: The ideal number.

Osha wrote:Take a disk image of Boom Blox Bash Party
Convert it to a (very long) integer.

Nice try, Osha, but in this thread we're only interested in the intrinsic properties of the number, not those that derive from its representation in some arbitrary base.

Kurushimi
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### Re: The ideal number.

Nobody post! There are 28 replies in this topic. It's perfect!

Wait, darn.

minno
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### Re: The ideal number.

Kurushimi wrote:Nobody post! There are 28 replies in this topic. It's perfect!

Wait, darn.

OK, now we stop at 30.
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squareroot1
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### Re: The ideal number.

But 30 isn't prime.

Kurushimi
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### Re: The ideal number.

Neither is 32.

But it is a power 2.

Macbi
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### Re: The ideal number.

As it turns out the "replies" column in the fora counts the amount of replies, not the amount of posts, so we now have 34 posts.
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Kurushimi
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### Re: The ideal number.

Another numbers I enjoy are 32768, 65536, 2147483648, and 4294967296.

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### Re: The ideal number.

squareroot1 wrote:But 30 isn't prime.
But it is primorial. And all composites <=30 share a common factor with 30.

Quaternia
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### Re: The ideal number.

2.
It's more the fear factor: every time I do something in number theory, I always offer thanks that it's the only even prime number
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### Re: The ideal number.

No love for 1?
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DarkRat
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### Re: The ideal number.

423

has 42 and 23 in it

doogly
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### Re: The ideal number.

mrcheesypants wrote:No love for 1?

One is the loneliest number.
LE4dGOLEM: What's a Doug?
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Keep waggling your butt brows Brothers.
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