A very easy one:
An oblong garden, half a meter longer than wide, consists entirely of a gravel-walk, spirally arranged, a meter wide and 3630 meters long. What are the dimensions of the garden?
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A very easy one:
An oblong garden, half a meter longer than wide, consists entirely of a gravel-walk, spirally arranged, a meter wide and 3630 meters long. What are the dimensions of the garden?
is this the topic of riddle freaks?
i love riddles, but not mathematic ones :p
ps.. anyone seen nemesis game? its an interesting movie on this subject.
cilu, i didn't understand your problem very well. I drew some scratch in M$ Paint to see if you agree with my understanding:
You got it pretty well.
Hmmmm! Ok I'll try to solve this one. I've seen it before in school, but long time ago hehe.
Long time, no answer... :confused: If this one is too hard (though it's so simple) I will post another... :sick:
Oh well, I seached the forums and found this long thread by chance, I am not boasting but I truly love humors and fun stuff,
I now have a tricky funny problem that I think would tease your mind sometimes especially on weekends like this. You can post anything about my problem, give me any ideas that you like to,
I have a multiset S (S1....Sn) and another set dS (S21, S31,....,Sn1,S32, S42,....Sn2,.....,Snn-1)
A multiset is a set whose elements can be repeated whereas in a set,its elemest cant.
For example, S={2,1,4,3} => dS={-1,2,1,3}
From dS, tell me all of the ways you think up to build up S again ???
Quote:
Originally Posted by cilu
half a meter longer then wide
That's not enough. What are the dimensions?
Well, what does S21, S31 etc. stand for? I.e. there seems to be a way of deriving dS from S, but how? From your example, it doesn't seem to be the multiplication of the items in S, so what is it?Quote:
Originally Posted by Hediea
you problem is wrong:
multiset S(S1....Sn)
set dS(S21, S31,....,Sn1,S32, S42,....Sn2,.....,Snn-1)
multiset S has N elements
set dS has N-1 + N-2 +... + 1 elements, that is SUM[i=1, N-1] (i) = N*(N-1)/2.
If N = 4, then dS should have 6 elements, but in your example both S and dS have 4.
If dS has 4 elements, there is no integer solution for N.
So, give us a valid example.
the valid dS seems pretty obvious to me:
For example, S={2,1,4,3} => dS={-1,2,1,3, 2, -1}
As it seems that Smn = Sn - Sm
that's how it starts anyway, until he has forgotten or removed the duplicated elements (that he should not have done given dS is a multi set).
Smn = Sn - Sm was obvious from the very first moment. However, I was expecting a valid example. He did not say enything avout removing duplicate entries...
Well, dS is not a multiset, so you can't have duplicates, so his example is valid.
A first observation is that you won't be able to get the exact multiset S back, since you can always add or remove a constant. Another thing is that since S is a multiset, you can have lots of different solutions in S for a given dS.
For example, say you are given the dS of {-1, 0, 1}
S could be: {2, 1, 2}
Or it could be: {2, 1, 2, 1, 2}
Or it could be: {3, 2, 3, 2, 3, 2, 3}
etc.
Here's a pretty interesting problem. The reason I pose it here is that both my friend and I solved it independently: I solved through a long, mathetmatical route, while he solved via a comparatively quick logic-based route.
Suppose there is a row of k lightswitches, each wired to its own lightbulb, and initially off. Someone turns on one of the lightswitches randomly. Then they toggle another lightswitch randomly (if it's the same one as the first one, the light goes off. Otherwise a second light comes on). This process is repeated n times (so that n total toggles are made). What is the expected value for the number of lights that will be on when the process is complete, in terms of n and k?
(I have tried to make this as clear as possible; unfortunately I won't be around until Sunday to clarify ambiguities I have overlooked)