# 5 horse track , 25 horses puzzle

For 25 Horses,  5 horse track,
No stopwatch provided ,
How many races are required to determine the 3 fastest horses ?

Split the horses into 5 groups and race each of the 5 groups (5 races) After that, we have the horse placements :

A B C D E
1 1 1 1 1
2 2 2 2 2
3 3 3 3 3
4 4 4 4 4
5 5 5 5 5

You can eliminate all 4’s and 5’s from the chart, since we know that there are at least 3 horses that are faster for each 4th and 5th place horse.

A B C D E
1 1 1 1 1
2 2 2 2 2
3 3 3 3 3

Now race all the 1’s (race #6). This will give you the fastest horse from the initial 25. But what about 2nd and 3rd place?

Approach it this way: which horses can we eliminate? Find all horses that we know have at least 3 horses faster than them. We can eliminate D1 and E1, because we know that A1, B1, and C1 are all faster than them. We can also eliminate all other horses in columns D and E below them. We can’t eliminate C1, but we can eliminate C2 and C3. We also eliminate B3, since B2, B1, and A1 were all proven to be faster.

A B C D E
1* 1 1
2 2
3

The only horses left to race are A2, A3, B1, B2, and C1. (Race #7). The 2nd and 3rd place finishers are then 2nd and 3rd fastest from the original 25.