A LETTER sent by Alan Turing to the eight year old daughter of an academic colleague is set to go up for auction next month.

The letter was sent from Turing's Adlington Road home, Wilmslow, to Maria Greenbaum daughter of his Jungian analyst Dr Franz Greenbaum, explaining with the aid of three diagrams the moves needed to play out successfully at solitaire. It is expected to fetch between £40,000 and £60,000 at Bonhams.

Turing's instructions includes three diagrams, and he explains: "I find it helps, if I am trying to do the puzzle to use four kinds of pieces like this (see diagram) or better still to use a board with the squares in four colours. Each piece always stays on the same colour until it is taken."

In the hand written letter in July 1953, Turing, who is credited with breaking the Enigma code during the Second World War, tells the youngster:"You start with only four x's and you must still have on [sic] at the end so you must be very careful of them, But there are 12 o's to be got rid of. One needs to remember this all the time".

"In the best of moves the number shows the piece to be taken and '-' means it is to be taken by a move horizontally, and 'I' that it is vertical."

The letter was first brought to public attention by Turing' mother Sara in her pioneering memoir of her son: "It must have been the childish streak in Alan which made him so much liked by and at home with children."

The letter included a postcard sent the summer before Turing took his own life. In March 1952, he had been brought to trial for conducting a sexual relationship with a young Manchester man.

Although he was open about his sexuality and was at pains to tell everyone that he saw no wrong in his actions, in order to avoid prison, he elected instead to undergo injections of the hormone oestrogen, a form of chemical castration.

Maria recollected: "I grew very fond of him and he was always very friendly. He eventually became more of a family friend than a patient of my father. I remember him having dinner with us often. After dinner he would sit on the floor with me while I played Solitaire.

"I thought it was so nice. He was a very warm person who always took an interest in what I was doing. I grew very attached to him... He had quite a stammer and bit his nails. He could be described as hyped up. But I always remember him as kind and friendly."