25 horses 5 tracks 5 fastest horses puzzle
Q: 25 horses, 5 race tracks. How many races you have to run to select top 5 horses.
Solution:
Step 1: First, we group the horses into groups of 5 and race each group in the race course. This gives us 5 races.W11 W12 W13 W14 W15W21 W22 W23 W24 W25W31 W32 W33 W34 W35W41 W42 W43 W44 W45W51 W52 W53 W54 W55Step 2:we race the 5 level 1 winners(w11,w21,w31,w41,w51) and assume winning order of this race is w11,w21,w31,w41,w51 (THIS IS 6TH RACE)
Step 3: BECAUSE WE NEED TOP 5 AND W51 HAS COME 5TH Position that is the reason we don’t need to consider W52 W53 W54 W55
now we have
now we have
W11 W12 W13 W14 W15W21 W22 W23 W24 W25W31 W32 W33 W34 W35W41 W42 W43 W44 W45W51
Step 4: because we need top 5 then dont need W25 W34 W35 W43 W44 W45
now we have
W11 W12 W13 W14 W15W21 W22 W23 W24 W31 W32 W33 W41 W42 W51
Step 5: top 1 is already achieved which is W11(winner of 6th race)
remaining are
remaining are
X W12 W13 W14 W15W21 W22 W23 W24 W31 W32 W33 W41 W42 W51
Step 6: candidates for 5th position: W51 W42 W33 W24 W15. 1 RACE TO GET 5TH POSITION (this is 7th race)
remaining are
X W12 W13 W14 W21 W22 W23 W31 W32 W41
Step 7: candidates for 4th position: W41 W32 W23 W14. 1 race to get 4th position ((this is 8th race)
X W12 W13 W21 W22 W31
Step 8: candidates for the 2nd and 3rd position: W12 W13 W21 W22 W31. 1 race to get the 2nd and 3rd position ((this is 9th race)
Hence answer is 9 races.