# 25 Horses 5 Tracks 3 Fastest Horses Puzzle

Puzzles:

25 horses, 5 race tracks. How many races you have to run to select top 3 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   W55`

Step 2:we race the 5 level 1 winners(w11,w21,w31,w41,w51) ans assume winning order of this race is w11,w21,w31,w41,w51

Step 3: BECAUSE WE NEED TOP 3 AND W41 HAS COME 4TH Position that is the reason we don’t need to consider W41   W42   W43   W44   W45 and also W51   W52   W53   W54   W55
now we have

`W11   W12   W13   W14   W15W21   W22   W23   W24   W25W31   W32   W33   W34   W35`

Step 4: because we need top 3 then don’t need W14   W15   W24   W25   W34   W35

now we have

`W11   W12   W13W21   W22   W23W31   W32   W33`

Step 5: because in 6th race W31 has come on the 3rd position that is the reason we do not need to consider W32, W33 and also we will not consider W23
now we have

`W11   W12   W13W21   W22W31`

Step 6:  top 1 is already achieved which is W11(winner of 6th race)
remaining are

`W12   W13W21   W22W31`

Step 7: now race W12 w13 w21 w22 w31 to get the 2nd and 3rd winner