I was going to post the answer tonight but I'm gonna be lazy and wait till tomorrow. That will give everyone one more day to do something else :D
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I was going to post the answer tonight but I'm gonna be lazy and wait till tomorrow. That will give everyone one more day to do something else :D
Okay, okay! Enough suspense! Now for the result that no one has been waiting for...
Well, I guess souldog's distillation sums up the best way to look at the problem in my opinion, though you could look at it as a sequence enumeration problem (where you look for sequences with no meaning-neutral subsequence and map them over the relations), but it would be a real pain to work out. Now, there is a canonical method to solve for the order of groups described through free generators and a presentation of relations known as the Todd-Coxeter coset enumeration, but I never seem to use it (its really straightforward, but it seems to me to be as much work as the alternative for small cases like this).
The answer was 12. Here's how I would solve it. First, as souldog points out, there are two relations on one generator: momomo = ni and lolo = ni. But if you look at the other relationship in the presentation you will notice that you can get some really nice reduction formula from it by slowly moving syllables over to the other side. You get
Those come in really handy. Now since we don't need to look at anything with lolo or momomo in it, we will just start listing everything without them. Let's list everything up to 5 syllables to start withCode:molomolomolo = ni
molomolomo = le = lo
lomolomolo = me = momo
molomolo = lomomo
lomolomo = momolo
molomo = lomomolo
lomolo = momolomomo
molo = lomomolomomo
lomo = momolomomolo
where I have gone through and used whatever obvious set of relations from those derived above to get the equalities. All the equalities are to words of lesser number of syllables. Since all 5 syllable words have lesser syllable equivalents, a simple induction shows that all larger words are equivalent to a word of four syllables or less (since they contain 5 syllable subsequences). So the ones that don't have lesser equivalents are the only possibilities. There are twelve of them. At that point, I just did a multiplication table and brute forced out the 144 possibilities. No two rows or columns were equivalent (you actually don't need to do anywhere near all of the table to find this out, but I was having too much fun...), and therefore none of the words were equivalent. Thus the answer.Code:ni
mo
lo
===========================
momo
molo
lomo
===========================
momolo
molomo
lomomo
lomolo
===========================
momolomo
molomomo
molomolo = lomomo
lomomolo = molomo
lomolomo = momolo
===========================
momolomomo = lomolo
momolomolo = molomomo
molomomolo = momolomo
molomolomo = lo
lomomolomo = molomomo
lomolomomo = momolomo
lomolomolo = momo
Okay... someone else's turn!
To change, i'll post an easy one:
A doctor goes to a party among a lot of other guests. Just after the punch was served, he receives an emergency call. He immediately finishes his drink and leaves. When he comes back, some time later, every one is dead. The analysis reveals the poisoned punch is the reason of their death.
Why didn't the doctor die?
was the doctor's drink actually punch?
The doctor finishes his drink just after the punch was served. But you don't say if 'his drink' is punch or not. I suppose the doctor's drink is not punch because he leaves just after the punch is served.
Is this the reason why the doctor did not died?
The doctor has been drinking punch as well.
Doctor Luz. Are you giving in Simon666's like avatar?
Noooo.
It's me after trying to solve the last galathaea's question. ;)
[this is a joke]
Could this have been a kind of posion that dissolves under a great deal of pressure (that the doctor must've felt with his patient whereas the calm other guests died) ?
The doctor puts the poisson into the punch?
And fakes the call...Quote:
Originally posted by Doctor Luz
The doctor puts the poisson into the punch?
I want a logical answer not some... urban fairy tail that can be explained in a million ways. If it's like that I'm not counting it as a point.
you still don't have the answer. But I've never heard of a poison that dissolves into stress! :D:D
I think its a very logical possibility. But surely there are more than one possible explanation (more ore less credible).Quote:
Originally posted by SeventhStar
And fakes the call...
I want a logical answer not some... urban fairy tail that can be explained in a million ways. If it's like that I'm not counting it as a point.
OK
For me there are only 2 possibilities
First the punch was poisoned after the doctor left but thats just a guess.
Second the doctor was poisoned too but eventually he took some kind of antidote maybe because of working wiyh an ill patient or he was just checked for infections when he got to the hospital...
Anyway I couldn't figure out a straight answer but maybe the second one will satisfy you
Nope, that's not it.