Question

Thomas bought a train set with 25 toy engines that run at different speeds. The train set has five parallel tracks that can be built to race the engines. After each round, Thomas notes down the relative speeds of the engines instead of their actual lap times. What is the least number of races he can play before he can decide the first, second and third fastest engines?

Your Answer​

Answer 1

Answer:-

Thomas needs 7 races to find the engines.

Question:-

• There are 25 toy engines.
• We can only compare the speed, and race up to 5.
• We need to find the first, second and third fastest engines.
• Minimum trials are required.

Solution:-

1st~5th trial

We first group 5 engines each from the 25 engines, then race them.

We can identify the fastest engines of each group.

6th trial

Then we race the fastest five.

If the engines won 4th or 5th, such engines are at most 4rd~5rd fastest, so the group is eliminated.

If the engine won 3rd, the engine is at most 3rd fastest one. So, we eliminate the group except for the engine.

If the engine won 2nd, the engine is at most 2nd fastest one. So, we eliminate the group except for the engine and the one behind it.

If the engine won 1st, the engine is the fastest one. The two behind have a possibility to become the 2nd and the 3rd, so we eliminate except them.

7th trial

Now there remain 5 engines. We race them for the last time and find the 1st, 2nd engine from them. Then, they will be 2nd and 3rd because we already have the fastest engine. So, we're done!

Answer 2

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• he will first do five races, then he'll get winner from all of the 5 races

• Then again he' ll do the race between them and he'll get positions of horses

• Hence, it needs minimum 7 races

So, YOUR ANSWER IS 7

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hope it helps