Birthday problem

The workings

Everyone has at least once in their life attended a friend or family member’s birthday party and has probably sung the well-known and famous song “Happy Birthday To You”, considered the most popular song in the world and one of the most hummed songs according to the 1998 Guinness Book of Records.

The story of this song is a peculiar one. In 1893, American sisters Mildred and Patty Smith Hill, nursery teachers in Louisville, Kentucky, wrote a book of songs for the children in the kindergarten where they worked. The first song, entitled “Good Morning to All”, was a simple song to greet the children: “Good morning to you, Good morning to you, Good morning, dear children, Good morning to all”.

One day, when it was the birthday of one of their pupils, one of the sisters, Patty, decided to keep the melody and change the lyrics to “Happy Birthday to You”, thus giving birth to this famous song.

In 1924, the song was published in a songbook by Robert Coleman, and later became popular through radio and movies. It was then that the third of the Hill sisters, Jessica Hill, proved that the original song was the work of her older sisters, and in 1934 she obtained the copyright.

Well then, today’s workings is about birthdays. But not just any birthday, but one that should be celebrated as it deserves by all the regular readers of this section. It is no other than the birthday of the debut of the IMUS Blog in society. This section of the Blog’s divertimentos has already completed or will soon complete (today’s problem is precisely about answering this question) 3 years, in which more than 60 problems of all kinds have been proposed, analysis, calculus, logic, geometric, algebraic, probability, entertaining, etc, which, according to the opinions received by the coordinators, have been to the full satisfaction of all those who have tried to solve them.

For all these reasons, in this introduction, which is somewhat longer this time than on previous occasions, the coordinators of Divertimentos con delantal, apart from congratulating ourselves on this third year of the section, wish, above all, to thank all the readers who have sent in their answers to the proposed problems for their participation. To all of them, thank you very much.

The fun

Three friends, Javi, Juan and Manolo, all mathematicians, want to celebrate the third anniversary of the presentation of the IMUS Blog by a mutual friend, Antonio, also a mathematician, but neither Juan nor Manolo can remember the exact date of the event with any certainty. Javi remembers it well, but instead of giving it to them, he suggests that they use their mathematical knowledge to deduce it from a clue he is going to give them and from the comments they can make when they receive it.

To do this, he gives them a list of 10 possible dates:

2 September	3 September	6 September
4 October	5 October
1 November	3 November
1 December	2 December	4 December

and tells one of them the day and the other the month of that presentation, individually and separately, without each of them being aware of their conversation with the other. He then allows each of them to make some comments about that conversation.

These comments were as follows:

Juan: I don’t remember when that presentation was, but now I know that Manolo doesn’t remember either.

Manolo: Initially I didn’t remember when the celebration was, but now I do.

Juan: Then I know that date too.

The question is: On what day and month did the presentation of the IMUS Blog take place?

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Solution

We encourage the readers to try to solve the divertimento for themselves. Whether you succeed or not, you can always consult the solution in this link.