suppose u have a race-court and 25 horses. you can make run only 5 horses at a time or in one race and you have to choose the fastest 5 among them. so, minimum no. of trial or races in which you can surely choose the best 5 is.......... .
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Race all 25 horses in 5 group races. Then race the winners (1st place winners) of the previous 5 races in the 6th race. The last race should be run by :
1) the 2nd place 🏇 from the 6th race
2) the 3rd place 🏇 from the 6th race
3) the 2nd place 🏇 from the 6th race's 1st place 🏇 previous (or first) race
4) the 3rd place 🏇 from the 6th race's 1st place 🏇 previous (or first) race
5) the 2nd place 🏇 from the 6th race's 2nd place 🏇 previous (or first) race
To be honest, these 7 races can't actually give you the best 5 horses, just THE BEST 3.