# 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
`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
`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)