You have 25 horses. how many races do you need to find the fastest 3 horses? you don't have a timer, and you can run only 5 horses per race

• 7 races.
  
  first 5 races ( ABCDE)with any 5 horses in each race.
  Rank horses as (A1,A2..A5), (B1,B2,..B5)...,(E1,E2..E5)
  Then 6th race with winners (A1,B1,C1,D1,E1)of all five races.
  say the result is A1,B1,C1,D1,E1 in the order.
  Winner of 6th race (A1) is fastest among 25 horses.
  
  Next two horses will be from A2,A3,B1,B2,C1 and 7 th race among these 5 horses will give next two fastest horses.
• 11 years agoHelpfull: Yes(20) No(33)
• 8 races.
  
  first 5 races ( ABCDE)with any 5 horses in each race.
  Rank horses as (A1,A2..A5), (B1,B2,..B5)...,(E1,E2..E5)
  Then 6th race with winners (A1,B1,C1,D1,E1)of all five races.
  say the result is A1,B1,C1,D1,E1 in the order.
  Winner of 6th race (A1) is fastest among 25 horses.
  
  Now we took the Next faster of the Group A
  who is now A2...........
  
  next race (7th) race is between A2,B1,C1,D1,E1 :--------RESULT may be D1 won
  
  so the D1 is the Second Faster
  
  now we took the next from the D Group(which comes 2nd in the race of d1,d2,d3,d4,d5) it is D2
  
  
  D2,A2,B1,C1,E1 part in the 8th race and we Found the 3rd Highest . . . . .
• 11 years agoHelpfull: Yes(20) No(23)
• 7 races
  
  Let’s say that we have 5 races of 5 horses each, so each row in the table above represents a race. So, “X1 X2 X3 X4 X5 ” represents a race, and “X6 X7 X8 X9 X10 ” represents another race, etc. In each row, the fastest horses are listed in descending order, from the fastest (extreme left) to the slowest (extreme right). The fastest horses in each race are the ones on the left – so in the first race X1 was the fastest and X5 was the slowest. In the second race X6 was the fastest, X7 was the second fastest and so on.
  
  Only 5 horses each race
  So, now we ask ourselves: what do we know after these 5 races? Well, we do have the 5 five fastest horses from each race (X1, X6, X11, X16, and X21). But, does that mean we have the 5 fastest horses? Think about that for a second. Well, actually it does not mean that we have the 5 fastest horses. Because, what if the 5 fastest horses just happened to be in the first race – so X1 X2 X3 X4 X5 are the fastest horses. X1, X6, X11, X16, and X21 are all the fastest horses in their individual groups, but there could be one group that just happened to have all of the fastest horses. Remember we haven’t compared all the horses to each other since we can only run 5 horses in a race, so that is still a possibility. This is very important to understand in this problem.
  
  Work through a process of elimination
  
  Well, now that we’ve had 5 different races, we can eliminate the slowest 2 horses in each group since those horses are definitely not in the top 3. This would leave these horses:
  X1 X2 X3
  X6 X7 X8
  X11 X12 X13
  X16 X17 X18
  X21 X22 X23
  
  
  We also know the 5 fastest horses from each group – but it’s important to remember that the 5 group leaders are not necessarily the 5 fastest horses. So what can we do with that information?
  Well, we can race those 5 horses against each other (X1, X6, X11, X16, and X21) and that would be the 6th race. Let’s say that the 3 fastest in that group are X1, X6, and X11 – automatically we can eliminate X16 and X21 since those 2 are definitely not in the top 3.
  
  What other horses can we eliminate after this 6th race? Well, we can automatically eliminate all the horses that X16 and X21 competed against in the preliminary races – since X16 and X21 are not in the top 3 then we also know that any horse that’s slower than those 2 is definitely not in the top 3 either. This means we can eliminate X17 X18 X22 and X23 along with X16 and X21.
  
  Now, we also know that X1 is the fastest horse in the group since he was the fastest horse out of the 5 group leaders. So, we don’t need to race X1 anymore. Are there any other horses that we can eliminate from further races? Well, actually there are. Think about it – if X6 and X11 are the 2nd and 3rd fastest in the group leaders, then we should be able to eliminate X8 since X6 raced against him and he was in 3rd place in that race. X7 could only possibly be the 3rd fastest, and since X8 is slower than X7, we can safely eliminate X8. We can also eliminate X12 and X13 since X11 was the 3rd fastest in the group leaders, and X12 and X13 were slower than X11.
  So, all together we can eliminate these horses after the 6th race: X17 X18 X22 X23 X16 X21, X12, X13, X8 and X1. This leaves us with the following horses to determine the 2nd and 3rd fastest horses:
  X2 X3
  X6 X7
  X11
  
  
  
  This means we only have 5 horses left! Now we race those horses one more time – in the seventh (7th) race – and we can take out the top 2 horses and that would mean we have the 2nd and 3rd place horses! So, we have found our answer! It takes 7 races to find the top 3 horses in this problem.
  
  
  
  
  
  
  
• 9 years agoHelpfull: Yes(5) No(0)
• Answer is 6 races
  
• 11 years agoHelpfull: Yes(4) No(7)
• 6................... First 5 races have 5 winners..................nd then those 5 horses run a race and we can have 3 fastest horses.
• 11 years agoHelpfull: Yes(4) No(10)
• 11......it is very lengthy process......
  1.first conduct 5 races for 25 horses...select 1,2,3 horses from each race.
  2.conduct another race all first position,second,third horses and select 1,2,3 from that..now we have 9.
  3.send 5 horses in a race and select 1,2,3 positions...once again conduct a race for remaining 4 horses+3rd position horse of previous race...select 1,2,3 positions..now we have 5 horses..
  4.finally conduct a race to those 5 horses...by u can get fastest 3 horses..
  ans is 11..
• 9 years agoHelpfull: Yes(3) No(1)
• @aman
  
  What u gave was the exact solution. Great.
• 11 years agoHelpfull: Yes(2) No(21)
• 6 races..
  5 horses per race
  20+(1 won horse)---1st race
  16+(1 won horse)---2nd race
  12+(1 won horse)---3rd
  8+(1 won horse)---4rth
  4+(1 won horse)---5th
  6th last race...
• 10 years agoHelpfull: Yes(2) No(1)
• There Are Total 25 Horses( At Beginning ). If They Can Be Divided In 5 Different Groups So That There Will Be Exactly 5 Horses In A Group.Keep Racing These 5 Groups.i.e, Total Races = 5. Now From Each Races 3 Will Be Selected.Total Selected = 3*5 = 15, Which Can Be Further Made 3 Groups Of 5 Horses.After Racing Them,Total Races = 5+3 = 8, We Will Have Total 9 Horses Left.Which We Can Further Divide Into 2 Groups (1 Group Will Be Of 5 Horses,2nd will Be Of 4 Horses). We Are Said Only 5 Horses Will Race.So In This Case Only 1st Group Will Race. Total Races = 8+1=9.Now 3 Horses will Came From The Race's End.We'll Have 3+4=7 Horses Left, Which Can Be Divided Into (5,2). Again 1st Group Will Race.Total Races = 9+1 = 10. We Will Left With 5 Horses After The Race.And Finally We Will Race Again ,i.e, Total Races = 10+1 = 11.And We Will Find The Best 3 Out Of 25.Answer Is " 11 Races"
• 6 years agoHelpfull: Yes(2) No(0)
• @bharat Wrong answer.
• 11 years agoHelpfull: Yes(1) No(18)
• answer is 6 races.
  first 5 races for all 25 horses grouped 5 in each race and 1 race for all the selected horses who won the race and top 3 are selected.
• 9 years agoHelpfull: Yes(1) No(2)
• answer is 18
  becoz we cannot find 5 fastest horses from just 5 heats.eg.if winner of heat1 can be slower than third ranker in heat3.
  u have to find each winner seperately
  conduct 5 heat of 5 horses.select fastest one from each heat.now u have 5 selected horses
  fastest horse will be among them for sure.conduct race between them.winner is the fastest horse.
  now u have 24 horses left.we have to find second fastest.conduct another 5 heats among 24 horse.simulating above process u will get second fastest horse..now from 23 horses do the above process u will get 3 rd fastest horse.
  total races
  to select fastest horse=6
  to select second fastest=6
  t oselect 3rd fastest=6
  total races=18
  
• 9 years agoHelpfull: Yes(1) No(1)
• The answer is 6.
  
  5 horses * 5 races
  
  Which will give 5 winners.
  
  Next race between the winners.
  
  and then we will get fastest 3
• 11 years agoHelpfull: Yes(0) No(10)
• first of all race 5 times with five horses.Winner of all 5 five horses to race them .first three will be the winners
• 10 years agoHelpfull: Yes(0) No(2)
• answer is 6.
• 10 years agoHelpfull: Yes(0) No(1)
• answer is 6
• 9 years agoHelpfull: Yes(0) No(1)
• 6 races we need to find the fastest 3 horses
  
• 9 years agoHelpfull: Yes(0) No(1)
• 8 races are required
• 9 years agoHelpfull: Yes(0) No(0)
• ans is 6.
  first run 5 horse and again 5 horses and so on.
  one horse selected from each race.
  and then run 5 selected horses.
• 8 years agoHelpfull: Yes(0) No(0)
• 6 races
  five races will give five winners and 6th race will be among the five winners which will give 3 fastest horses
• 7 years agoHelpfull: Yes(0) No(0)
• initially first race, choose the horse which comes first, similarly from 4 more races choose the horse which comes first(the one which runs the faster) at the end choosing best 3 among the last 5 horses choosen
  
  minimum 5 races and maximum 6
• 3 years agoHelpfull: Yes(0) No(0)