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(#5287892) Re: 25 horses
Posted by FragileKitty on 1 Oct 2021 at 1:24PM
It takes 7 races to determine the fastest 3 horses.

Given 25 horses, name them 1 through 25. To make it easier for illustrative purposes, let each horse's name be its "speed" (but in general we don't know this yet).

Hold 5 races with different horses in each race.

Race 1: 1,2,3,4,5
Race 2: 6,7,8,9,10
Race 3: 11,12,13,14,15
Race 4: 16,17,18,19,20
Race 5: 21,22,23,24,25

The top 3 of each race remain in the running (15 total), so we've eliminated 10 horses.

Eliminated: 1,2,6,7,11,12,16,17,21,22

Remaining:

3,4,5
8,9,10
13,14,15
18,19,20
23,24,25

Next we'll race just the 5 winners:

Race 6: 5, 10, 15, 20, 25

This eliminates 5 and 10 (and the horses they beat).

We know now that 25 is fastest, so we can remove it from subsequent races, and now we only need to find the two fastest horses remaining.

This leaves:

14, 15
19, 20
23, 24

We can remove 14, because 20 beat 15, which beat 14. This leaves us with:

15,
19, 20
23, 24

Race 7: 15, 19, 20, 23, 24

23 and 24 win, so they join 25 in the top three.
div>Replies to this message:
SubjectPosted ByDate & Time
5287907Re: 25 horses FragileKitty1 Oct 2021 2:13PM
5287906Re: 25 horses Jools1 Oct 2021 2:05PM
5287904Re: 25 horses Dragon Jr1 Oct 2021 2:02PM
5287903Re: 25 horses Jools1 Oct 2021 2:01PM
5287892Re: 25 horses FragileKitty1 Oct 2021 1:24PM

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