Thanks cm27874 for the info. Yes I got the same Solomon W. Golomb's 10- vertex graph. However Moser Spindle is quite interesting.

<t>This is some Olympiad problem ( I don't know the source ) :You have three colors - say Green, Red and Yellow. Is it possible to color (using all three colors) the unit radius circular disk such that distance between any two points of the same color is never one unit!We can have a tricky solution(...

<t>Hi,"There is a pile of twelve coins, all of equal size. Eleven are of equal weight. One is of a different weight. In three weighing find the unequal coin and determine if it is heavier or lighter." This problem is quite common I guess. I just tweaked the problem a bit as " There are 12 coins but ...

<t>1st show : 2013 divides r,=> 2014^2013-1=(2013)^2*kand r=(2013)*kNow rewrite , 2014^r-1 =2014^(2013*k)-1=(2014^(2013)-1)*[ (2014)^2013*(k-1) + ... + (2014)^2013+1]=k*((2013)^2)*[ (k*(2013)^2+1) ^ (k-1)+...+(k*(2013)^2+1)+1 ]RHS above is divisible by k^2 as well as (2013)^2 [Since k divides (k*(20...

Thanks wileysw... It seems I've got it what I wanted ....

Thanks outrun , Yes ... I have also mentioned it ... However I am trying to find is there any intuitive solution ( may be using plane euclidean geometry) possible! someone from here could help....

<t>I was trying to generalize a particularly easy puzzle :We have a line A on the plane , and two fixed point P & Q on the same side of the line, then what is the point R on the line A such that QR+PR is minimum.This is relatively easy to solve and could be solved using plane euclidean geometry....

Thanks katastrofa,Can I get any online paper or article regarding this, this will be of great help.

<t>Hi All,while calculating the proportional returns of a CDX IG series, should we consider only series change( On the Run/Off the Run) or version change of the index as well.To elaborate more, say trd(t) is the spread level of CDX IG at time t(days), if I look into the 10-day proportional return re...

<t>QuoteOriginally posted by: AlanThat clarifies it. "Assume any arbitrary relationship" is quite different than saying "we don't know the relationship".The relationship is arbitrarily chosen from the class of all possible relationships, but once chosen -- it is revealed tothe booking agent, right?....

<t>QuoteOriginally posted by: wileyswalghosh, to answer the general version in your old post:suppose m>=2n+1, convert the question to a graph by connecting two people if either hates the other. the question is if each vertex has degree >=m but total edges <= m*n, prove it is (2n+1)-partite, or equiv...

<t>QuoteOriginally posted by: AlanThe problem seems mis-stated to me. Otherwise, if there is more than 1 person in a room, and you don't know the haterelationships, then the probability of a killing is > 0. Since that was ruled out, it doesn't make sense.Yes we don't know the relationships... And do...

I don't know whether the solution I found is elegant or not .... but answer is quite interesting .... its way below 29....

<t>QuoteOriginally posted by: frenchXThe "hate relationship" is known or unknown by the book manager ? (I suppose it's known otherwise I don't see a solution)Unfortunately or may be fortunately it is unknown... only known fact is each person hates exactly three others... but why cant there be any so...

<t>QuoteOriginally posted by: frenchXDo you really want with a 100 % occurence than no one gets killed or does the killing enters your cost function ? (I know I'd be a pitiful hotel manager )1st priority would be that no one gets killed as well you dont want to book 57 rooms . Suppose 10 is optimal ...