How many minimum races does it take to select 3 top horses out of 9 if only 3 race tracks are available.

• for first time 3 tracks -3 horses
  second time 3 tracks-3 horses
  third time 3 tracks -3 horses
  by calculating the time we can select the thee top horses
• 12 years agoHelpfull: Yes(3) No(1)
• the answer for this question is 7.
  sol->
  we have total 9 horses and 3 tracks this means only 3 horses can run at a time.
  so we make triplets say X(X1,X2,X3),Y(Y1,Y2,Y3),Z(Z1,Z2,Z3)=>3 races. After these three races we will get 3 horses say (X1,Y1,Z1).Now again perform a race(4th)we came to know who is first. suppose X1 is the first but Y1 and Z1 are not 2nd and 3rd actually this may happen that set x may have another faster horse.for ex. if in the 4th race Y1 was 2nd then it is faster in the set Y and set Z(bcs Z1 was at 3rd)=>5th race with remaining 2 horses of set x.now Z1 was 3rd so it is faster in the set z only =>2 races 1 is with remaining 2 horses of set x and 2nd is with remaining 2 horses of set y.So minimum 7 races.
• 12 years agoHelpfull: Yes(3) No(1)
• 3 races is the wrong answer ......the answer for this question is 7
• 12 years agoHelpfull: Yes(1) No(0)
• i think to select top 3 horses if 3 tracks r available is (9c3)...
  i.e. (9*8*7/1*2*3)coz 4 selecting 3 horses from 9 which has to run on the those 3 tracks are done by 9c3 ways or 84 ways..
  or we get different combination of 3 horses in 84 ways,then only we can find which one is beter than which one &hence find the top 3 of them.
  
  acc. to MR. Manish we not guarantinely get the top 3 ,we r sure 4 best one only bt dont sure that those are best 3
  for eg-if we take a triplet in which top 3 horse r there then after the race we eliminate 2 better horses than other
  
• 12 years agoHelpfull: Yes(0) No(0)