Briefly

Playing to be Sherlock Holmes

Playing to be Sherlock Holmes

In June 2001 I had to go to renew my identity card, which had already expired for a couple of months. It is one of those things that one has to do sooner or later, so the other day I was all ready to plant my thumbprint there and leave until I found myself at the police station with a queue of about fifteen people, all of them Waiting to renew your card or get your passport. A true heaviness. Anyway, patience.

In front of me was a woman with an orange bag that apparently got bored as much or more than me, so we started complaining about hanging out:

  • I don't know why they can't put more people, if they see that now before the holidays everyone wants to renew their card. Make us wait here, with this heat ... - She said.
  • Of course, of course - I replied - because I have to go and they could hurry up. Of course you have to understand them, all day filling in the same thing ... - I said that because I don't like to hurry the poor either.
  • Well, that's why. If they have been like this all day, they could have a little more practice, right? That I have to go to Chiclana this afternoon with my sister and I still don't have the bags packed, you know? When I said it, I noticed that he had an Cádiz accent and asked him why - Yes, in my family we are all from Cádiz! I was there until I was fourteen and then I came to Granada, and my sister went to Malaga. Since then we alternate visits every three years: one I go to Malaga, another I invite her here to my house, and the third we both go to Chiclana to see my parents. We have done that since we left Cádiz; I remember the summer we spent with my parents when I was seventeen ... I love that beach ...

    - At that moment he seemed to remember the tail, and said - Let's see if they finish already and I can leave at once!

There were only three people left in front of us; Three or four more minutes.

  • You know? When I was eighteen I made my identity card. Since then I have renewed it promptly every five years, as it should be, and I have never had to wait so long. Today everyone has agreed to come, huh? She said.
  • Yes, it seems.

We were waiting a little longer and when there was only one person left in front of us they gave us the form to put our data (“fill in this, and sign here, here and here”). As we wrote, I saw casually that the woman I had been talking to was called Amparo and that I was born on February 29. "Wow, curious day," I thought. We finished, we delivered the forms and the photos, we put the mark where it corresponded and we cleaned ourselves with a washcloth that they gave us. I told the woman that until later, I wished she had a good time at the beach with her sister and I kept thinking while I was going home that truly, Amparo seemed much younger than she really was.

How old was Amparo?

Extracted from www.matematicas.net

Solution

As Amparo was born on February 29, we know that in 2000, the last leap so far, he reached a multiple age of four, that is, currently, June 2001, he has an age that is a multiple of four plus one.

Since he goes to Chiclana every 14 years and goes to Chiclana this year, his age minus 14 must be a multiple of 3.

Since the ID is renewed every five years from age 18, your current age minus 18 must be a multiple of five.

Of the first condition, taking into account that he is of legal age, his age could be 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65 ...

For the second condition of the previous ages 29, 41, 53, 65, 77, 89, 101, 113, 125, 137, ...

Finally, for the third condition only 53, 113, 173, ...

Considering that Amparo's parents still live and that spending a hundred years is currently rare, the age sought is 53 years.