Enigma 394: Unwinding
From New Scientist #1544, 22nd January 1987 [link]
Professor Kugelbaum was unwinding at the Maths Club with a cigar after lunch when a wild-looking man burst in and introduced himself thus:
“My name is TED MARGIN. Juggling with the letters of my name one obtains both GREAT MIND and GRAND TIME. But I digress. Each letter of my name stands for one digit exactly from 1 to 9 inclusive and vice versa. And, do you know,
(A × R × M) / (A + R + M) = 2,
MAD is greater than ART (though RAT is greater than either), and TED = MAR + GIN.
If, in addition, I were to tell you the digit which corresponds to M then you could deduce the one-to-one correspondence between the letters of my name and the digits 1 to 9″.
At this point a helpful butler removed the man, but Kugelbaum was amused to find that the information was quite consistent.
Write the digits 1 to 9 in the alphabetical order of the letters to which they correspond.