Answer Posted / hacker

Solution: the answer is 7 races.

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 W15

W21 W22 W23 W24 W25

W31 W32 W33 W34 W35

W41 W42 W43 W44 W45

W51 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 W15

W21 W22 W23 W24 W25

W31 W32 W33 W34 W35


Step 4: because we need top 3 then dont need W14 W15 W24 W25 W34 W35

now we have

W11 W12 W13

W21 W22 W23

W31 W32 W33


Step 5: because in 6th race W31 has come on 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 W13

W21 W22

W31

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

W12 W13

W21 W22

W31

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



Hence answer is 7 races.

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