27 horses race. 5 each race. What is the minimum number of races to find the 5 fastest ones?
My approach:
1st round: 5 races for a total of 25 horses, leaving out horses #26 and #27.
find the fastest 5 from those 5 races
$\begin{bmatrix}1 & 2 & 3 & 4 & 5\\6 & 7 & 8 & 9 & 10\\ 11 & 12 & 13 & 14 & 15 \\ 16 & 17 & 18 & 19 & 20\\ 21 & 22 & 23 & 24 & 25 \end{bmatrix}$
suppose #1,6,11,16,21 as fastest 5 horses.
2nd round: 1 race with the fastest 5 to find the fastest one. Suppose #1 is the fastest.
3rd round = 7th race = race #1 with #26,#27, #6, #2 and suppose the first 4 are exactly the fastest four.
4round = 8th race = #2,#7,#11. Suppose #2 wins.
So total of 8 races to find as fastest 1,26,27,6,2. If you change winners of the 3rd round you could actually get to 10 races, but the question ask for the minimum number of races.
What do you think?