Who killed David?

The workings

Many years ago, the Sociedad Andaluza de Educación Matemática SAEM THALES (Andalusian Society of Mathematical Education) published a series of booklets aimed at secondary and high school students in the schools and colleges of the province of Seville, in one of whose sections the brilliant detective O’Thales, specialised in solving all kinds of obscure cases based on his mathematical knowledge, solved with the help of his faithful assistant Mathson all kinds of brainteasers that the authors of these booklets proposed to the students.

In a certain and modest way, O’Thales was following in the footsteps of the famous English detective Sherlock Holmes, a character created in 1887 by the Scottish writer Arthur Conan Doyle, who stood out for his intelligence, his skilful use of observation and deductive reasoning to solve difficult cases, as well as his predecessor, the character Auguste Dupin, created by Edgar Allan Poe. Well, to celebrate the thirtieth anniversary of the completion of these fascicles, we have rescued a problem from one of them, slightly modified in its wording, which is as follows.

The fun

Detective O’Thales and his assistant Mathson were asked by the police to help them solve a mysterious murder that had taken place a few years earlier.

A wealthy industrialist named David had been killed in a bomb blast that had completely destroyed a huge mansion he owned, to which he had retired after having been involved in dubious business ventures that had brought him a lot of profit. The police had closed the circle of suspects to David’s seven ex-wives, whom he had invited to spend a few days at his mansion before his death.

Newspapers at the time reported that in his will, also lost in the explosion, David had left nothing to any of his seven ex-wives.

“I remember this case,” said O’Thales. “The curious fact is that the bomb was specially designed to be hidden under the pillars of the room where David slept, which means that the assassin had to make several visits to the manor in order to detonate it.”

“Absolutely,” said Mathson, “which is why I interviewed them all. And they all swore to me that they had never been to that castle more than once in their lives.”

“Perhaps one of them is lying,” replied O’Thales. “Did you ask each of them for the days they spent there?”

“Yes, but unfortunately, after all these years, none of them could remember the exact dates. However, each of them did remember which other wives they had seen there during their stay. This is what they told me: Ana saw Benita, Carlota, Felisa and Georgina; Benita saw Ana, Carlota, Elisa, Felisa and Helena; Carlota saw Ana, Benita and Elisa; Elisa saw Benita, Carlota and Felisa; Felisa saw Ana, Benita, Elisa and Helena; Georgina saw Ana and Helena; and Helena saw Benita, Felisa and Georgina.
You see, my dear O’Thales? The answers agree with each other.”

Then O’Thales, after a few moments’ thought and some scribbling on a piece of paper, replied:

“Happiness, Mathson! What you have just told me leads me uniquely to the murderess.”

The question is: who killed David?

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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.