The ages of the four daughters

The workings:

Taking advantage of the fact that one of the protagonists of today’s divertimento is a mother of four daughters, I wanted to draw attention to one of the most serious problems facing Spain: the very low birth rate. Since 1975, the birth rate has halved from around 19‰ to just over 9‰; so much that in 2016 there were more deaths than births. If the trend does not change, the inversion of the population pyramid will create serious problems not many years from now – for example, the collapse of the retirement system. The rise in the birth rate experienced during the first decade of this century was cut short by the crisis and the disastrous job prospects for young people. The government should do something to correct these expectations, in addition to tackling other related issues… improving the network of nurseries and nursery schools, tax incentives for births, etc. And it is overdue, because reversing these birth rate statistics takes time.

The fun:

Manuela, a mathematician (M), meets in the street an old friend, Antonia (A), whom she has not seen for quite some time, and the following dialogue is established between them:

– (M): Hello, how are you? Long time no see.

– (A): Yes, it’s true. It’s been many years. In all this time, I’ve got married and I already have 4 daughters.

– (M): Oh yes, and how old are they?

– (A): Well, as you’re a mathematician, you’ll have to calculate them. I’ll give you two clues: the first is that the product of my daughters’ ages is 48, and the second is that, curiously, the sum of those ages is the number of the bus that’s standing right there in front of you.

Manuela thinks for a few seconds, glances at the bus, thinks again for another few seconds and says to Antonia:

– (M): These two clues are not enough. I need you to give me some more information.

And Antonia replies:

– (A): Well, I’ll tell you that the little girl has blue eyes.

With these data, could you calculate the age of Antonia’s four daughters, which Manuela did immediately?

 

 

 

 

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.