Jnyusa wrote:
Hobby, your link is German.
I could sort of follow what they were saying, but I wasn't confident that I really understood.
In Faramond's post I just looked at his number series and saw they were powers of two in descending order.
Yes, it's German - I just posted it because of the box where you can have any numbers switched to a different system, not because of any explanation it provided! Sorry about the misunderstanding!
There's a box where you can enter digits, and then you pick a system from which, and a system into which you want to change it - for example an octal (or whatever the word in English might be - a system based on powers of 8 ) "35647" would be "3232213" in a system that uses powers of 4 etc etc. I just posted it to show that even though I looked up how this stuff worked (because I didn't remember from school) I didn't do the actual maths on this one myself!
But, yes, like you said, it could be based on any system.
So - not sure if anyone still needs an explanation, but here goes (and my apology to the resident mathematician for the probable crudeness of this
):
We happen to use a system based on 10 different digits, so that we only need to add a new digit for each power of ten:
1
10
100
1000
When you have the decimal number 523 that just means you have 5 "hundreds", 2 "tenners" and 3 "ones".
If you had only four digits to use, you'd have to figure out how many "fours", "sixteenths" etc you have in the number instead.
If you have two digits to use, you need to add a digit for each next power of two - I've always found it easiest to imagine that the one is "yes" and the 0 is "no" on a string of numbers.
1 = 1
10 = 2
11 = 2 + 1 = 3
100 = 4
101 = 5
etc.
At school we had a little piece of cardboard on which we'd written:
1024 512 256 128 64 32 16 8 4 2 1
So if the task was to write down the number 523 we could just look at it and write:
1000001011
To transfer any number back into decimal, you have to start multiplying and adding from right to left:
The digit on the right is the rest, so it's just that digit.
The second one is whatever system you are using multiplied by whatever number it is: n*x
The third is n*n*x
etc.
For example, in a system of eight:
35647
is
(8*8*8*8*3)+(8*8*8*5)+(8*8*6)+(8*4)+7 = 15271 in decimal.
Quote:
Also, given the answer you provided ... it would not necessarily have to be a binary answer, would it? It could, for example, be the sum of the powers of three, or five? One would discover that by trial and error? - or is there an easier way to look at that and know the referent number system.
That's a good question! I guess if you see no digit higher than 3 you could guess that it's a system of 4 that's being used - but of course it might just as well be a coincidence that there was no higher digit in a decimal number.
However, other systems than binary and decimal aren't really in use (apart from hexadecimal, of course).
Quote:
I didn't start at the beginning, because the permutations are endless and I get headaches easily.
I started with the letters p and q - hoping there would be some - because p is the only letter with 4 zeros and q is always followed by u, which makes a rather long series. Lucikly there were both, and I was able to work backwards and forwards from those letters.
Wow, thanks - yes, that should be helpful! After 15 minutes I had enough variables to wear out my patience! Very clever way of approach!
_________________
Artwork by Breogán - thank you, my friend!
Eine Blume der Asche meines Herzens
but being a cheerful hobbit he had not needed hope, as long as despair could be postponed.