From: LANDSBERG@sbhep2.phy.sunysb.edu (Greg Landsberg)
Subject: Re: zagadka
Organization: SUNY at Stony Brook
Date: Thu, 24 Dec 1992 22:40:17 GMT
X-News-Reader: VMS NEWS 1.20

In <85800@ut-emx.uucp> alexei@hagar.ph.utexas.edu writes:

> One day came Ivanushka Durachok to Zmey Gorynych and challenged him for
> a combat (he wanted to free some captive maiden in distress...) 
> -- This is going to be a battle of wits, said Zmey, and I will set the
> rules as follows:
>    There are 10 wells with enchanted water in my garden, and though the
>  water seems ordinary, whoever drinks of it turns into a frog (in a 
>  little while). But the water of each well with higher number can act
>  as a counterspell for the water of wells with lower numbers. (Say,
>  if you drink once from the well No.3 and then from the well No.6, you 
>  will survive. There is no remedy for the water of the 10th well.)
>    We will go in the garden, in secret fill our glasses with water, and 
>  then each will take a drink from the glass of another. Then we are 
>  free to go and drink all we want, BUT, my servants will prevent you 
>  from approaching the 10th well, which I reserve for my exclusive use
>  (Zmey was'nt a fool.)
> -- Agreed, said Ivanushka (he was a fool, after all), and everything
> went according to the rules.
>    In a little while, to the general surprise and consternation of
> the public <vsego chestnogo naroda>, Zmey Gorynych became a frog, and 
> Ivanushka married the princess (and they lived happily ever after.) 
>    Question: how did this occur? 
>    Remarks: Zmey was'nt a fool; there are no other poisons and counter-
> spells around; solution does not involve little green men from Mars, etc.
> 
> This zagadka is a little bit too long and involved, but you will be
> really pleased if you arrive to the answer by yourself (this is also
> a good test whether your solution is the real one; my friends liked it.)
> Happy holidays! 
> 					Alexei Beklemishev.

Yes, it  is nice  but to solve  it takes  much less  time than  to read it.
However, it is  not completely  defined, so I assume  that the words ``Zmey
wasn't a  fool'' mean that he  gave  Ivanushka ``Love  Potion number 9'' or
number 10,  because there are no  counterspells against  these two types of
water  available to  Ivanushka (i.e,  1..9). And,  of course,  Zmey himself
drinked potion number 10 after  drinking from Ivanushka's glass in order to
cancel  the  action of any   poisonous waters  in the  garden  available to
Ivanushka. After this assumption the solution is truly simple:

Ivanushka drank potion number one  BEFORE drinking from Zmey's glass (while
secretly filling  his own glass).  After that he just  cancel the action of
this  potion by  water  number 9 or  10 from  Zmey's  glass.  That's how he
survived.

In order to kill  Zmey he also did a  very simple  trick: he filled his own
glass with FRESH WATER (well, we believe that there were a lot of fountains
in Zmey's garden). After drinking from Ivanushka's glass without any poison
Zmey drink  his own  deadly potion  number 10 and   successfully kicked the
bucket.

If there was no fresh  water in the garden, we  may consider the mixture of
potions say,  number 3 and 6 as a  ``fresh water''  because they suppose to
cancel each other  (however, this is  not completely  correct, because this
'group' is non-Abelian  and the result of  cancelation depends on the order
of drinking; well we may assume that  Ivanushka made a ``Bloody Mary'' with
potion number 6 on the bottom *smile*).

Have a nice holidays!

Cheers,

Greg
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