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February 7th, 2003, 09:48 AM
SolarFlare
Quote:

Originally posted by SeventhStar
operators are just operations and some of them are sort of indexes like it's between x and y. but that's a big clue and I wont tell you any more...

I can't seem to figure out what this means.

The 'operators' either
- perform one standard operation each (by standard, I mean can be expressed with one symbol, such as * / + - ^, etc.)
- act as an index, in which case the numbers still get multiplied together (because it's like there's no operator between them)
Well then, if this is the case, there either must be a lot of "index operators" or else some of the operations are repeated.

Probably everything I just said is wrong... now I'm really confused.
February 7th, 2003, 09:51 AM
Simon666

I was thinking for example that y in p1yp2p3 could mean:

p1 * ( p2 + p3)

Thus imply some sort of order, while

( p1 * p2 ) + p3

would be a different result ofcourse. Perhaps it is something like that.
February 7th, 2003, 09:58 AM
SolarFlare

I don't think that's what 'y' does, because it is involved in too many prime numbers. I think it's probably simple subtraction.
February 7th, 2003, 02:21 PM
galathaea

Wow! I've looked at this thread from time to time, but you guys are crazy!!! The current problem is great! I just wish I had time to work on it...

I'm just going to grab the problem off and work on it at home this weekend, since I don't want the surprise spoiled (and it looks like solarflare is almost there and I don't want to see his answer!)
February 8th, 2003, 05:30 AM
Simon666

Quote:

Originally posted by solarflare
If anyone else wants to work on it but can't find a place to start, I have proven that 'barwon'=1, 'ganal'=33, and 'hul'=6.

If you are correct I would like to make a few additions. It can help, though I'm still stuck.

Code:

Solved: 39 = ganalibarwonhul 199 = barwoniganalhul Unsolved: 14 = farokobarwonhul 29 = omaryhutarhul 37 = babumbarwonhul 48 = babusgutarhul 52 = farokadonzesgutarhul 59 = babutfarokhul 64 = gutaragutarhul 71 = urukigutarhul 89 = barwonybabuhul 106 = omarifarokhul 112 = gutarobabuhul 128 = omarturukhul 149 = ganalsurukhul 208 = barwonadonzemganalhul 233 = gutarmomarhul 242 = donzemomarhul Starting from urukigutarhul = 71 gutar=11 uruk = 5 gutar=10 uruk = 11 gutar= 9 uruk = 17 gutar= 7 uruk = 29 gutar= 5 uruk = 41 gutar= 4 uruk = 47 gutar= 3 uruk = 53 Starting from omarifarokhul = 106 farok = 17 omar = 4 farok = 16 omar = 10 farok = 15 omar = 16 farok = 13 omar = 28 farok = 12 omar = 34 farok = 11 omar = 40 farok = 10 omar = 46 farok = 8 omar = 58 farok = 5 omar = 76 farok = 4 omar = 82 farok = 3 omar = 88 farok = 2 omar = 94 Impossible: farok = 1 omar =100 because farok = 1 = barwon farok = 6 omar = 58 because farok = 6 = hul farok = 7 omar = 64 because omar = 64 = gutaragutarhul farok = 9 omar = 52 because omar = 52 = farokadonzesgutarhul farok = 14 omar = 22 because farok = 14 = farokobarwonhul gutar = 1 uruk = 65 because gutar = 1 = barwon gutar = 2 uruk = 59 because uruk = 59 = babutfarokhul gutar = 6 uruk = 35 because gutar = 6 = hul gutar = 8 uruk = 23 because gutarhul = 48 = babusgutarhul
February 9th, 2003, 11:29 PM
galathaea

what I've got...
This is a tough problem, and my two days have not netted me any conclusions. This is a huge set of parallel operator equations and the nature of the operators is not very well specified, and it is hard to make a lot of progress into them. But I see everyone is sharing their work so we can all figure it out (which I think would be more fun than getting the answer...), so I wanted to share what I have found out so far. Much of it seems to have already been found out by solarflare, but I wanted to show the manipulations involved, because I think they are illustrative.

First, I noticed that the numbers requested could be built from the rules we already knew, so that it was not necessary to actually solve any of the operator equations prior. This is because 178 = 29 + 149 is an element of {S + S} and 189 = 48 + 52 + 89, 351 = 48 + 71 + 242, and 372 = 52 + 112 + 208 are elements of {S + S + S}. So we get the names
- omaryhutarhuliganalsurukhul (178)
- babusgutarhulifarokadonzesgutarhulibarwonybabuhul (189)
- babusgutarhuliurukigutarhulidonzemomarhul (351)
- farokadonzesgutarhuligutarobabuhulibarwonadonzemganalhul (372)
Now I found the first two by playing around with the numbers and the last two I had to be more systematic and enumerated the 3-partitions of the last digits in the partition summing to 0, 10, or 20 + the last digit of the target sum. I think there is some good algorithms out ther for automating this type of thing if it pops up later...

Now, I normally approach these type of problem by brute force at first until certain patterns make themselves more familiar to me. So I decided to systematize the names with abstract labels. My first chomskian parse of the words has led me to:
- farok = A
- barwon = B
- hul = C
- omar = D
- hutar = E (?)
- babu = F
- ganal = G
- gutar = H (?)
- donze = I
- uruk = J
for the object labels and
- o = (a)
- y = (b)
- m = (c)
- s = (d)
- a = (e)
- t = (f)
for the operators. I am concerned about the hutar / gutar parsing because the original question seems to say that two different "words" would not have the same root. The three possible explanations I have are: the "h" in hutar is a mistype, I have misunderstood the "root" rule, or "g" and "h" are operators on "utar". The latter would significantly change my analysis so far, but I have done some analysis in the other 2. Translating the known decompositions under the above abstract labels and ordering by operation, I get:

Code:

(+) pairs G(+)B(*)C = 39 J(+)H(*)C = 71 D(+)A(*)C = 106 B(+)G(*)C = 199 (a) pairs A(a)B(*)C = 14 H(a)F(*)C = 112 (b) pairs D(b)E(*)C = 29 B(b)F(*)C = 89 (c) pairs F(c)B(*)C = 37 H(c)D(*)C = 233 I(c)D(*)C = 242 (d) pairs F(d)H(*)C = 48 G(D)J(*)C = 149 (e) pair H(e)H(*)C = 64 (f) pairs F(f)A(*)C = 59 D(f)J(*)C = 128 triples A(e)I(d)H(*)C = 52 B(e)I(c)G(*)C = 208

From this I saw the same thing solarflare must have seen, which is the two (+) pairs that involve B, C, and G. Since (+) is a known operator (unlike the (a) - (f) operators), this seems a good system to start with. This system solves to

Code:

G = 39 - BC C = (39 +/- sqrt(39^2 - 4B(199-B))) / (2B)

Now I brute force tested the endpoints and came up with two possible solutions: B = 1, G = 33, C = 6 or B = 1, G = 6, C = 33. I have some heuristics for choosing the first one (as solarflare has), but I still don't have a definitive proof for either one.

Looking at the two remaining unsolved questions, I see I have to find out the objects B, D, and I as well as the operators (b), (d), and (e). (e) has a very interesting member relationship with H to itself that seems a possibility to attack. H also has relations to D and I through the (c) operator. If E and H are the same (possibility of mistype) then there is an additional D relationship to H through the (b) operator. Thus there seems sufficient information to solve for the latter name question if we can figure out the operators.

This is where I think we all might be having problems. Its hard to figure out enough operators to test out and a brute force enumeration. I'll give a list of all the types I've been trying out. I think it was very important the mention of intervals as the center of the language's reasoning, and SeventhStar said something very cryptic about it being something like between X and Y. I came up with
- distance -- eg. 20(dist.)25 = 5
- forward reflection -- eg. 30(fr.)33 = 36
- backward reflection -- eg. 17(br.)22 = 12
- midpoint -- eg. 44(mp.)56 = 50
- addition -- eg. 65(+)31 = 96
- lattice count, multiplication -- eg. 12(*)20 = 240
- modulo circle mapping -- eg. 32(%)15 = 2
But I would love to know what possibilities you all are thinking about. This is currently where I am at. I'm trying out various operators on the 3 equations I mentioned earlier to see if I can crack the second name 1st.

Where is every one at? Let's all share and try to figure it out, cause its huge!
February 10th, 2003, 12:57 AM
galathaea

a little more info

The reason I use distance in the above is because it is guaranteed to be nonnegative, which I believe SeventhStar mentioned as the domain of analysis for the operators. However, what is your reasoning solarflare on your conclusion about 'y'? This is extremely important for solving D(b)H(*)C = 29 if H=E.

I have also checked operators that are linear operators like the placement operators of normal number systems

Code:

A(forward lin.)B = AC + B A(backward lin.)B = A + CB

so each operator may be distinguished by a direction and a multiplier. But then the given equations are not complete enough to specify the result (I believe, from dimensional analysis). So I haven't had much success in this direction.

Also, I have tried index operators into Fibonacci codes. Something like

Code:

A(fib. #n)B = 11...A 1s.. 100...n 0s...011...B 1s...1

but now I think that might be kind of silly. The reason I was think of this was because the sum and multiplication of the size of 1 runs have some special properties in Fibonacci code, which could have been a reason for the number system (and can basically said to be a number system of intervals).

I have been trying to figure out (e) for some time because of the H relationship I mentioned earlier, and I could see where it could be several operators (giving me different H). This (e) is important because it is found in both triples given and the one triple asked for (name #1). It seems to have some special operation that can be used (possibly unambiguously? -- order of operations) with another operation. If anyone has made progress on this I would love to know their reasoning.

SeventhStar, if you could comment on hutar/gutar, it would help me alot. Is the 'h' a mistype or are h and g separate operators? Or is the analysis where they are different correct?
February 10th, 2003, 06:07 AM
Wfranc

Whowwww

S Galathaea! You are really great !!!
February 10th, 2003, 06:49 AM
SeventhStar

Re: a little more info

Quote:

Originally posted by galathaea
...
SeventhStar, if you could comment on hutar/gutar, it would help me alot. Is the 'h' a mistype or are h and g separate operators? Or is the analysis where they are different correct?

Oh my god!!! I'm sososososo sorry!!!!!! I've missed this. there is no 'hutar' it's 'gutar'.... :rolleyes:
I'm really sorry guys... My I'm a stupid ********. Sorry.
February 10th, 2003, 06:53 AM
Simon666

Re: Re: a little more info

Quote:

Originally posted by SeventhStar
Oh my god!!! I'm sososososo sorry!!!!!! I've missed this. there is no 'hutar' it's 'gutar'.... :rolleyes:
I'm really sorry guys... My I'm a stupid ********. Sorry.

I already requested if there were spelling errors. :rolleyes: Are you sure there aren't any further? Like "i" instead of "y" or vice versa?
February 10th, 2003, 06:59 AM
SeventhStar

Well i just checked it for a 100th time and there are no more mistakes. Sorry! Really! :( :(
And I'll post the answer tommorow. If you want me to do it today just tell me...
February 10th, 2003, 12:09 PM
galathaea

I vote for tomorrow at least, as I'd really like to work out some options. However, I haven't been an active member of this thread, so I'd defer to the real participants. I still want to work this out, as I haven't had a good abstract algebra problem to practice on in some time... :)
February 10th, 2003, 05:16 PM
SolarFlare

Re: what I've got...

Quote:

Originally posted by galathaea
Now I brute force tested the endpoints and came up with two possible solutions: B = 1, G = 33, C = 6 or B = 1, G = 6, C = 33. I have some heuristics for choosing the first one (as solarflare has), but I still don't have a definitive proof for either one.

Starting with G+BC=39, and B+GC=199:

B+GC=160+G+BC
B+GC-G-BC=160
(G-B)(C-1)=160
(G-B)=160/(C-1) (Eq.1)

also, (again from the original 2 equations)
G+BC+B+GC=238
(G+B)(C+1)=238
(G+B)=238/(C+1)

Now prime factoring 238 gives
238=2*7*17

Since the sum of positive integers is a positive integer, (238/(C+1)) must be a positive integer, meaning C+1 is a factor of 238, meaning C+1=2,7, or 17, meaning C=1,6, or 16.

Letting C=1 makes Eq.1 invalid. Letting C=16 gives (from Eq.1) G-B=160/15, which is not a whole number. The difference of integers is an integer, so this cannot be.

This leaves only C=6. Solving for the other variables gives B=1, G=33. There is no other solution.

As for all the other random stuff in the problem, I have made no progress in the minutes I have spared to work on it. :(

Quote:

Originally posted by SeventhStar
Oh my god!!! I'm sososososo sorry!!!!!! I've missed this. there is no 'hutar' it's 'gutar'....
I'm really sorry guys... My I'm a stupid ********. Sorry.

Shame on you... but I'll accept your apology. I think the problem is equally hard with or without the typo ;).
February 10th, 2003, 06:05 PM
galathaea

Quote:

Originally posted by solarflare
Since the sum of positive integers is a positive integer, (238/(C+1)) must be a positive integer, meaning C+1 is a factor of 238, meaning C+1=2,7, or 17, meaning C=1,6, or 16.

Unfortunately, the correct implication is that C+1 is one of the 8 divisors of 238 (1, 2, 7, 14, 17, 34, 119, or 238) and 33 is not then excluded. This makes me want to keep both options open, which is quite a pain!
February 10th, 2003, 06:28 PM
SolarFlare

Quote:

Originally posted by galathaea
Unfortunately, the correct implication is that C+1 is one of the 8 divisors of 238 (1, 2, 7, 14, 17, 34, 119, or 238) and 33 is not then excluded. This makes me want to keep both options open, which is quite a pain!

Oops!

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