November 26, 2012

A puzzle of cycling

English version: Contrarreloj ciclista

The men's individual time trial of the UCI Road World Championship takes place today.

The trial participants start out one at a time

We know that among the first 30 participants, 15 are Americans and the other 15 are Europeans.

How many cyclists have to leave so that we make sure that there are 2 of the same continent racing the trial?

Simply 3 cyclists.

If the first 2 are from the same continent, either European or American, then they'll have fulfilled the condition of having 2 riders on the same continent performing the test.

And if they are from different continents, one European and one American, the third cyclist will necessarily coincide with one of the 2 first cyclists, since we know that in the first 30 participants there're no runners from other continents.

The only difficulty with this problem is to be aware of what is being asked. There are people who answer that we need 16 cyclists racing on the road, as they interpret the question the wrong way, and they believe that the question is: how many cyclists must be out to ensure that at least 2 cyclists from different continents are racing the trial?
So we conclude that if we want to answer the question correctly, we must pay a care attention about  which is exactly the question.

No comments:

Post a Comment