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7 Races required to find top 3 fastest horses.
- jemishsp June 03, 20141. First divide horses in group of 5. Let's say group name is G1,G2,G3,G4,G5.
2. Now 5 races required for each group. Lets say Horses are named as their ranking in a group. For instance fastest horse in G1 is named G1H1, second fastest in G1 is named G1H2 and so on. Do this naming scheme for all group. Till now you have done only 5 races.
3. 6th race will be among top horses of groups. Means G1H1, G2H1, G3H1, G4H1, G5H1. For instance result of the race is G3H1, G5H1, G2H1, G1H1, G4H1. Whoever wins this race will be fastest horse among 25 and it is G3H1. As G1H1 and G4H1 is not able to win 6th race, all the horses in G1 and G4 is not a candidate of top 3 horses. You can discard this two groups. As G3H1 comes first, G3H2 and G3H3 will be eligible for top 3 candidate. G5H1 comes second in 6th race, only G5H2 will be candidate for top 3. G2H1 comes third so no other horses from G2 will be eligible except G2H1.
4. So last race will be among G3H2, G3H3, G5H1, G5H2, G2H1. Top two horses from this race and G3H1 is top 3 horses among 25.