You are given 25 horses and a racetrack where only 5 horses can race at a time. You do not have any timers or stopwatches, so you can only determine the relative ranking of horses based on the results of each race. The goal is to determine the top 3 fastest horses using the fewest number of races.
Objective:
Find the fastest 3 horses using the minimum number of races.
Solution:
To solve this puzzle, we need to carefully plan how we conduct the races and evaluate the results to identify the top 3 horses. The goal is to minimize the total number of races required.
Step-by-Step Solution:
Step 1: Group the Horses into 5 Races
Since the track can only accommodate 5 horses at a time, start by dividing the 25 horses into 5 groups of 5 horses each and race them.
- Race 1: Group 1 (Horses A1, A2, A3, A4, A5)
- Race 2: Group 2 (Horses B1, B2, B3, B4, B5)
- Race 3: Group 3 (Horses C1, C2, C3, C4, C5)
- Race 4: Group 4 (Horses D1, D2, D3, D4, D5)
- Race 5: Group 5 (Horses E1, E2, E3, E4, E5)
Each race provides the relative rankings within that group. So, after the 5 races, we know the fastest horse in each group, but we still don’t know the top 3 overall.
Step 2: Conduct a Race Among the Winners
Now, take the winners of each group (A1, B1, C1, D1, E1) and race them. This will help determine the fastest horse overall and the order among the fastest horses.
- Race 6: A1, B1, C1, D1, E1
Let’s assume the outcome of this race is:
- 1st: A1
- 2nd: B1
- 3rd: C1
- 4th: D1
- 5th: E1
Now we know that A1 is the fastest horse, but we still need to determine the 2nd and 3rd fastest horses.
Step 3: Analyze Possible Candidates for the Top 3
At this point, we know that A1 is the fastest, but for the remaining positions, we need to consider the following candidates:
- From Group A: A2 (2nd fastest in the group)
- From Group B: B1 (2nd overall in the winners' race) and B2 (2nd fastest in Group B)
- From Group C: C1 (3rd overall in the winners' race)
We can eliminate the rest because they either lost their group races or didn’t place high enough in the winners' race.
Step 4: Conduct a Final Race to Determine the Top 3
Now, we need a final race to determine the 2nd and 3rd fastest horses. Race the following horses:
- Race 7: A2, B1, B2, C1
The outcome of this race will reveal the 2nd and 3rd fastest horses.
Final Answer:
After Race 7, the top 3 horses will be determined, with A1 as the fastest (already known from Race 6). The top 2 from Race 7 will be the 2nd and 3rd fastest horses overall.
