Hint to Puzzle #59: 25 Horses, Find the Fastest 3
59. You have 25 horses, you want to pick the fastest 3 horses out of those 25. In each race, only 5 horses can run at the same time. What is the minimum number of races required to find the 3 fastest horses without using a stopwatch?
The first stage is probably obvious, we races 5 groups of 5. Let's label them by the following scheme, that is all those that are in the first heat will be labelled A followed by a number representing where they came in their heat. So B3 came third in the second race, for example.
| Race | |||||||
| A | B | C | D | E | |||
| Position | 1st | A1 | B1 | C1 | D1 | E1 | |
| 2nd | A2 | B2 | C2 | D2 | E2 | ||
| 3rd | A3 | B3 | C3 | D3 | E3 | ||
| 4th | A4 | B4 | C4 | D4 | E4 | ||
| 5th | A5 | B5 | C5 | D5 | E5 | ||
Think how we've eliminated the every horse that finished below 3rd in it's own race what else we can eliminate, what else can we race?
It's significant to realise that in a knockout tournament the runner-up isn't necessarily the second best, the second best could have met the best in an earlier round and been eliminated.
Where next?
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