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 How it Started (Eve Did Talk) (Posted on 2003-12-10)
Ever wonder why women talk so much? It all started with Eve, and not only did she talk, but she kept on talking forever (if only through the generations of women to come).

The following equation, in which each letter represents a different digit, shows this phenomenon as an infinitely repeating decimal:
```EVE/DID=.TALKTALKTALKTALK...
```
What number does each letter represent?

 Submitted by DJ Rating: 4.1429 (7 votes) Solution: (Hide) There are a number of ways to show that 0.TALKTALKTALKTALK...=TALK/9999. I will not go into that detail here. So EVE/DID=TALK/9999. The equation will solve for integer values, certainly, if DID is a factor of 9999. The prime factors of 9999 are 3, 3, 11, and 101. The factors of 9999 of the form DID are 101, 303, and 909. Also we know that E < D. A great deal of experimenting with the other numbers shows that there is only one solution of this type: ```242/303=.798679867986... 0 1 2 3 4 5 6 7 8 9 I - E D V - K T L A ``` Of course, DID needs not necessarily be a factor of 9999. Rather, it must be a factor of 9999*EVE. Much more experimenting with all of the numbers shows that there is a second solution: ```212/606=.3498349834983498... 0 1 2 3 4 5 6 7 8 9 I V E T A - D - K L ```

 Subject Author Date solution K Sengupta 2007-03-05 04:15:50 re(4): Solution--not unique (computer program used this time) Richard 2003-12-10 18:10:26 re(3): Solution--not unique (computer program used this time) Charlie 2003-12-10 13:19:44 re(2): Solution--not unique (computer program used this time) Richard 2003-12-10 13:08:35 re(2): Solution--not unique (computer program used this time) Charlie 2003-12-10 11:35:46 re: Solution--not unique (computer program used this time) Charlie 2003-12-10 11:29:39 Solution (no computer program used) Charlie 2003-12-10 09:56:19

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