Can we use Maxima Minima in this case? If yes then how, can you please elaborate a bit more here on what you did here like how did you arrive at this* (I mean 4 and 5 are not the factors of 9 they are just 4 + 5 = 9 and in12 = 3+4+5 how did you arrive here?)* ? Appreciate the effort! Thanks. Saturday, August 4, 2012 2:08:15 PM UTC+5:30, Kristofer wrote: > > Given some N, you want to split it in terms t1, t2, ..., tn where each > term represents a cycle of arrows between circles. > The number of steps in the dance corresponds to lcm(t1, t2, ..., tn) and > this is what we want to maximize. > > For N = 9, you could split it into 4 and 5, giving lcm(4, 5) = 20 > For N = 12, you could split it into 3, 4, 5, giving lcm(3, 4, 5) = 3 * 4 * > 5 = 60 > For N = 15, you could split it into 3, 5, 7 giving lcm(3, 5, 7) = 3 * 5 * > 7 = 105 > > I am not really sure about the optimal strategy - the simplest is a brute > force but that's likely too slow for large values of N. > I suspect you need to split N into terms such that each term is on the > form P^x where P is a unique prime. > > On Sat, Aug 4, 2012 at 5:27 AM, Tejeshwar Singh wrote: > >> The director of Hind Circus has decided to add a new performance called >> the monkey >> dance to his show. The monkey dance is danced simultaneously by N monkeys. >> There are N circles drawn on the ground. There are N arrows drawn between >> the >> circles in such a way that for each circle, exactly one arrow begins at >> that circle and >> exactly one arrow ends at that circle. No arrow can both begin and end at >> the same >> circle. >> When the show begins, each monkey sits on a different circle. At each >> whistle of the >> ringmaster, all the monkeys simultaneously jump from one circle to the >> next, following >> the arrow leading out of the current circle. This is one step of the >> dance. The dance >> ends when all the monkeys have simultaneously returned to the circles >> where they >> initially started. >> The director wishes the dance to last as many steps as possible. This can >> be achieved >> by drawing the arrows intelligently. >> For each of the three values of N given below, what is the maximum number >> of steps >> that the monkey dance can be made to last by drawing arrows appropriately? >> (a) 9 (b) 12 (c) 15 >> >> PLS REPLY WITH A FIGURE TO HELP ME UNDERSTAND! >> >> -- >> >> >> >> > >
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