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Who killed the duke of Densmore?

I need to find the idea for solving this problem.

The shadow of a grisly murder is hanging over the otherwise idyllic coast near Craymouth: carbonized bodies of two men and a crocodile have been found in a tower of Densmore Castle on the Isle of White. All three died a year ago in the explosion of a charge skilfully connected to a light switch. The two men were Sir Jeremy Morse and his butler Stewart; the crocodile was just a pet.

During his last year, the duke had received eight visitors at this castle; each of them was brought first to the island and then back to mainland by a motor boat. None of them recalls the precise dates or duration of her stay, but each remembers with certainty whom else she had met on the Isle of White:

Felicia Wynn met Emily Healey and Ann Laybourn;
Cynthia Mansfield met Diana Macleod, Emily Healey, Ann Laybourn, Betty Townsend, and Helen Grimshaw;
George Blake met Ann Laybourn and Helen Grimshaw;
Diana Macleod met Cynthia Mansfield and Emily Healey;
Emily Healey met Felicia Wynn, Cynthia Mansfield, Diana Macleod, and Ann Laybourn;
Ann Laybourn met Felicia Wynn, Cynthia Mansfield, Georgia Blake, Emily Healey, and Betty Townsend;
Betty Townsend met Cynthia Mansfield, Ann Laybourn, and Helen Grimshaw;
Helen Grimshaw met Cynthia Mansfield, Georgia Blake, and Betty Townsend.

The testimony of each woman is confirmed by the others and collusion between any two is out of question: this is the work of a serious writer, not one of your Agatha Christies. The butler is declared the killer and his own death is supposed to have been accidental. The case is closed.

But then Detective Ralston pays a visit to his friend Cedric Turner-Smith, a professor of Mathematics at Merton College. The brilliant mathematician suggests that one of the eight visitors is the murderer: during her stay on the island, she had hidden in the vast cellars once, or perhaps several times, in order to prepare her evil deed.

And Graph Theory comes into play.


Solution Preview

Please see the attached Pdf and Excel files as well as the explanation below.

First abbreviate each name with its first letter (A through H), and draw the graph with A through H as vertices and an edge connecting two vertices when a meeting took place.

The subgraph for A, B, G, and H has a problem. If A never ...

Solution Summary

Who killed the duke of densmore is examined.