A Common Libel


  EVE
  --- = .TALKTALK...
  DID
Each letter represents a different digit, and the division represents a common fraction that can be written as a repeating decimal. What is the fraction?

Source: The Penguin Book of Curious and Interesting Puzzles, David Wells, 1992, #450.
[Taken from Ken's Puzzle of the Day March 20, 1995.]

Ken's solution (from the above source, slightly imperfect, as shown):
EVE/DID=TALK/9999, so DID must be a 3-digit factor of 9999, namely 101, 303, or 909.
  1. DID cannot be 101 because the fraction is a proper fraction and E could not be 0 or 1.
  2. If DID=909, then TALK=11*EVE, but the units digit of 11*EVE is E, and could not be K. So, DID is not 909.
  3. DID must be 303. EVE can only be (1*1) or (2*2). The only option which doesn't repeat, in the quotient, a digit which appears in the dividend is 242. So the answer is 242/303=.79867986...
Khiem V. Ngo solved it similarly.

As pointed out by bjames@skygames.com (Fletch) and Denis Borris, there is another solution: 212/606=.34983498...
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