Sunday, August 30

Henry Ernest Dudeney

Henry Ernest Dudeney (1857 - 1930) was born in the village of Mayfield, East Sussex, England. He was England's greatest composer of math and logic puzzles. Dudeney is best known for his publications of mathematical problems and pasttimes, some of which provoked serious mathematical research.

He came from a family which had a mathematical tradition and also a tradition of school teaching.

Henry learnt to play chess at a young age and soon became interested in chess problems. From the age of nine he was composing problems and puzzles which he published in a local paper. Although he only had a basic education, never attending college, he had a particular interest in mathematics and studied mathematics and its history in his spare time.

One of the most famous of his geometrical puzzles is the "Haberdasher's problem" (Cut an equilateral triangle into four pieces that can be arranged to make a square)

He was a near - contemporary of Sam Loyd, America's greatest puzzle expert and the two men frequently exchanged puzzles and ideas. Many of Loyd's and Dudeney's published puzzles show strong similarities, demonstrating how close their collaboration sometimes was.

One of his publications was "Amusements in Mathematics", you have here an example of one of his puzzles.

"The Ruby Brooch"

The annals of Scotland Yard contain some remarkable cases of jewel robberies, but one of the most perplexing was the theft of lady Littlewood's rubies. There have, of course, been many greater robberies in point of value, but few so artfully conceived. Lady Littlewood, of Rowley Manor, had a beautiful but rather eccentric heirloom in the form of a ruby brooch.
While staying at her town house early in the eighties she took the jewel to a shop in Brompton for some slight repairs.
"A fine collection of rubies madam" said the shopkeeper, whom her ladyship was a stranger.
"Yes", she replied; "but curiously enough I have never actually counted them. My mother once pointed out to me that if you start from the centre and count up one line, along the outside and down the next line, there are always eight rubies. So I should always know if a stone were missing".

Six months later a brother of Lady Littlewood's, who had returned from his regiment in India, noticed that his sister was wearing the ruby brooch one night at a county ball, and on their return home asked to look at it more closely. He immediately detected the fact that four of the stones were gone.
"How can that possibly be?" said Lady Littlewood. "If you count up one line from the centre, along the ede, and down the next line, in any direction, there are always eight stones. This was always so and is so now. How, therefore, would it be possible to remove a stone without my detecting it?"
"Nothing could be simpler", replied the brother. "I know the brooch well. It originally contained forty-five stones, and there are now only forty-one. Somebody has stolen four rubies, and then reset as small a number of the others as possible in such a way that there shall always be eight in any of the directions you have mentioned."
There wasn't the slightest doubt that the Brompton jeweller was the thief, and the matter was placed in the hands of the police. But the man was wanted for other robberies, and had left the neighbourhood some time before. To this day he has never been found.
The interesting little point that at first baffled the police, and which forms the subject of our puzzle, is this: How were the forty-five rubies originally arranged on the brooch? The illustation shows exactly how the forty-one were arranged after it came back from the jeweller; but although they count eight correctly in any of the directions mentioned, there are four stones missing.

Prove how clever you are and try to solve it.
I'd like to have comments with the solution. In any case, I´ll give you the solution in a next post in a few days. And if some of you are interested in these puzzles I´ll publish some more in the future.