light the first string at both ends and in the middle. So it will burn completely in 15 min as the fire is advancing in 4 ways irrespective of the burn rate.
If we do the similar analysis for 15 min, I think we won't be able to do so!, Again if the length is of 60min. For 0-30 min, the burn rate is 2/3m/minutes and for 30-60 it's 2m/minutes. If I burn it at 0, 30,60m position, then 30-60 meter part will be burnt in 7.5 minutes only. But 0-30 meter part will take 30/(4/3) i.e = 22.5 minutes. So, the complete string will burn in 22.5 minutes not 15. On Sun, Jul 10, 2011 at 1:26 AM, oppilas . <[email protected]>wrote: > Sorry, should have done it on paper properly!! > > Thanks! > > > PS: below is the mail which I was about to write thinking that total time > would not be 30 minutes if we burn it from both ends. > > > Ok > Suppose the length is 60meters. > For 0-L/2 we have burn rate of 2/3m per minute. So, total time L/2/(2/3)= > 45minutes. > And for L/2 to L, we have burn rate of 2m per min. So, Time for burning > 30-60 meters is 15 minute. > > Suppose, we light up both the ends. > Then After 15 minutes, L/2-L portion will be completely burn. And > For 0-L/2 portion, we would have burn total 2/3*15= 10meters. > Now, You are left with 10-30 (i.e total of 20 meter string) and it is > burning at both ends after 15 minutes. > So, remaining string will burn in (20)/(2*2/3) time i.e 15 minutes. Shit :\ > > > > On Sun, Jul 10, 2011 at 1:02 AM, Dumanshu <[email protected]> wrote: > >> The above posted solution is independent of the burning rate. I am not >> counting the minutes using the half burnt string. Instead, the fire is >> running and when the whole string is burnt, I am using the time. >> >> Say u light up a string from both ends, then irrespective of burn rate >> it should give 30 min. Because we have the choice to lit the string >> from either end and it burns completely in 1 hour. >> >> On Jul 9, 10:09 pm, "oppilas ." <[email protected]> wrote: >> > Yes, these solution are valid. But for them the burning rate of each >> string >> > must be constant. >> > Each piece of string takes exactly an hour to burn, but the burn rate is >> not >> > constant >> > Can't we have a string which take 45 minutes to burn till half length. >> > 0-L/2. And 15 min from L/2 to L. >> > >> > >> > >> > >> > >> > >> > >> > On Sat, Jul 9, 2011 at 8:57 PM, Dumanshu <[email protected]> wrote: >> > > @oppilas: >> > >> > > light the first string at both ends and in the middle. So it will burn >> > > completely in 15 min as the fire is advancing in 4 ways irrespective >> > > of the burn rate. >> > > when the first string is completely burnt, light the second string at >> > > both ends to get another 30 min. So, overall 45 min. >> > >> > > On Jul 9, 5:11 am, "oppilas ." <[email protected]> wrote: >> > > > You have 2 pieces of string of different, unspecified length, and >> some >> > > > matches. Each piece of string takes exactly an hour to burn, but the >> burn >> > > > rate is not constant. . The strings have different burn rates, and >> of >> > > course >> > > > you don't know the rates anyway. >> > >> > > > Using only the matches and the strings, measure 45 minutes. >> > >> > > > I have thought a lot but unable to find a solution for this problem. >> Can >> > > > someone please try it. >> > >> > > -- >> > > You received this message because you are subscribed to the Google >> Groups >> > > "Algorithm Geeks" group. >> > > To post to this group, send email to [email protected]. >> > > To unsubscribe from this group, send email to >> > > [email protected]. >> > > For more options, visit this group at >> > >http://groups.google.com/group/algogeeks?hl=en. >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Algorithm Geeks" group. >> To post to this group, send email to [email protected]. >> To unsubscribe from this group, send email to >> [email protected]. >> For more options, visit this group at >> http://groups.google.com/group/algogeeks?hl=en. >> >> > -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
